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Write the following series by using the sigma notation.
1+8+27+64+...+1000
 2 years ago
 2 years ago
Write the following series by using the sigma notation. 1+8+27+64+...+1000
 2 years ago
 2 years ago

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shegBest ResponseYou've already chosen the best response.2
\[1^3 + 2^3 + 3^3 +.....+ 10^3 = \sum_{1}^{10}N^3\]
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.4
$$ \sum \limits_{i=1}^{10} i^3 $$
 2 years ago

AditiMeowBest ResponseYou've already chosen the best response.0
I never Understood sigma notation Someone please Explain Me =)
 2 years ago

shegBest ResponseYou've already chosen the best response.2
see what i have written above i.e., answer
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.4
$$ \sum $$ This is a capital sigma. It's use is best illustrated by an example: $$ \sum_{i = 1}^4 \frac{1}{i} = \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{4}. $$ You begin by replacing the index (in this case, $i$) with the first value it takes on (iit's lower bound in this case, 1). You then proceed to the next number and keep doing this replacement until you are at the upper limit (in this case, 4). Finally, you add all these terms up.
 2 years ago

shegBest ResponseYou've already chosen the best response.2
in above expression it is sum of cubes of first 10 natural numbers
 2 years ago

AditiMeowBest ResponseYou've already chosen the best response.0
What is there on top ,bottom and left ?
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.4
Fool is always right :P :D btw I have to attribute the answer to Austin Mohr read here http://math.stackexchange.com/questions/81921/weirdelettersigma I was too tired to type when there is already a very good explanation ;)
 2 years ago

shegBest ResponseYou've already chosen the best response.2
bottom it is the range where bottom is the lowest value that N can have and at top u having the highest value that N can have
 2 years ago

barboatBest ResponseYou've already chosen the best response.0
Could you explain why you write 10 up there ?
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.4
10 is the number of terms or number of iterations
 2 years ago

shegBest ResponseYou've already chosen the best response.2
\[\sum_{N=1}^{10}N^3 = 1^3 +2^3 + 3^3 + 4^3 +5^3 + 6^3 + 7^3 + 8^3 +9^3 + 10^3\]
 2 years ago

barboatBest ResponseYou've already chosen the best response.0
for this series, 1+3+5+7+..+99 it would be sigma (2n1). and at the bottom it is r=1, right ? how do i get the top number ?
 2 years ago

shegBest ResponseYou've already chosen the best response.2
\[\sum_{n= 1}^{50}(2n1) = 1+3+5+7+....+99\]
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.4
this is arithmetic progression, how you find the number of terms in an A.P ? ;)
 2 years ago

barboatBest ResponseYou've already chosen the best response.0
using the formula Sn = n/2(a+l), right ?
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.4
I would never dare to doubt sheggy ;)
 2 years ago

shegBest ResponseYou've already chosen the best response.2
hahahaha buddy i just asked u
 2 years ago

AditiMeowBest ResponseYou've already chosen the best response.0
But Sheg why is that 50 at the top?
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.4
Yes barboat .. plug in the values of a and b and find n
 2 years ago

AditiMeowBest ResponseYou've already chosen the best response.0
\[\sum_{1}^{99}\] is'nt it like this
 2 years ago

AditiMeowBest ResponseYou've already chosen the best response.0
Sorry n =1 at the bottom
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.4
No, it's an arithmetic progression .. find the nth term
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.4
a = 1 last term = 99 , d = 2 what is n ?
 2 years ago

shegBest ResponseYou've already chosen the best response.2
aditi the total number of first 50 odd natural numbers are there so i had put 50 at the top
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.4
aditi you know about arithmetic progression ?
 2 years ago

shegBest ResponseYou've already chosen the best response.2
and the thing which fool is saying that is also another method which is mostly used............and the thing which i m saying as we are having small size so we can calculate easily
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.4
then use it :) and sheggy point of view is also the same .. 1,3,5,7 so what is the 50th odd number ?
 2 years ago

AditiMeowBest ResponseYou've already chosen the best response.0
i thought the top one was last term and bottom first term
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.4
No it is the number of iteration
 2 years ago

barboatBest ResponseYou've already chosen the best response.0
so, Sn= n/2 (100) ? but what do i write on the Sn side ? i cant solve it otherwise
 2 years ago

AditiMeowBest ResponseYou've already chosen the best response.0
WOW I dont Know Maths =D
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.4
number of times you want to execute the operation.
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.4
No you know maths .. don't give up so easy :)
 2 years ago

AditiMeowBest ResponseYou've already chosen the best response.0
which one is number of times you want to execute the operation.
 2 years ago

shegBest ResponseYou've already chosen the best response.2
hahaha,.............see in simple words it is number of odd numbers that u have to add
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.4
number of times you want to execute the operation is upper limit  lower limit..
 2 years ago

shegBest ResponseYou've already chosen the best response.2
ok gr8 so u have to work hard
 2 years ago

AditiMeowBest ResponseYou've already chosen the best response.0
I learnt AP without Sigma
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.4
you could write sigma notation in various ways
 2 years ago

barboatBest ResponseYou've already chosen the best response.0
so, Sn= n/2 (100) ? but what do i write on the Sn side ? i cant solve it otherwise
 2 years ago

shegBest ResponseYou've already chosen the best response.2
just purchase this book K.C.Sinha
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.4
AP is not sigma .. you will learn sigma probably while doing Riemann sums in definite integral
 2 years ago

AditiMeowBest ResponseYou've already chosen the best response.0
Ok i understood something =P Thanks Fool and Sheg =D Take My Medals =) here you go
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.4
but I knew back from standard VII or VIII during olympaid training and all, however I was never good then :P also no need to buy any book .. just follow OCW it's great resource :)
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.4
thanks but I think you did not understand it ? :/
 2 years ago

shegBest ResponseYou've already chosen the best response.2
\[99 = 1 + (n  1) \times 2\] \[99 1 = (n  1) \times 2\] \[98 = (n  1) \times 2\] \[\frac{98}{2} = (n  1) \] \[49 = (n  1)\] \[49+1 = n\] \[50 = n\]
 2 years ago

AditiMeowBest ResponseYou've already chosen the best response.0
i understood the question barboat asked =)
 2 years ago

shegBest ResponseYou've already chosen the best response.2
fool buy books by Dr. K. C. Sinha it will help u alot....the books written by him are simply awesome
 2 years ago

AditiMeowBest ResponseYou've already chosen the best response.0
books are so heavy , i would rather carry a Laptop =P
 2 years ago

shegBest ResponseYou've already chosen the best response.2
@ Barboat what is the formula for nth term of AP \[t_{n} = a + (n 1)d\] where \[t_{n}\] is the nth term a first term d common difference n number of terms
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.4
btw $$1+3+5+7+99 = \sum \limits_{i =5}^{45} (2n+11)$$ am I right ?
 2 years ago

shegBest ResponseYou've already chosen the best response.2
here nth term = 99, a= 1 d = 2 n = ? now plug in these values u will get n
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.4
I have read the classics Hall and knight in higher algebra sheggy ;)
 2 years ago

barboatBest ResponseYou've already chosen the best response.0
isnt the formula Sn=n/2 (2a+(n1)d) ?
 2 years ago

shegBest ResponseYou've already chosen the best response.2
btw indians can also write some classics
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.4
sorry buddy I hurt to say but I don't agree . most indian authors plagiarized these classics :(
 2 years ago

shegBest ResponseYou've already chosen the best response.2
barboat b4 applying that formula u have to apply nth term formula for finding out number of terms
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.4
Do you know abut the famous Kanetkar books for C and datastructure ?
 2 years ago

shegBest ResponseYou've already chosen the best response.2
i too carry the same feelings as u but not in case of K. C. Sinha. and in case of finance books i never refer indian authors. I prefer to read other than indian publication house books
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.4
I don't know about finance but I haven't found any in my domain ..
 2 years ago

shegBest ResponseYou've already chosen the best response.2
yeah i had found in fiance domain but the master of finance field is also from india and whole world is reading his books only and due to whom i had been to this website
 2 years ago

FoolForMathBest ResponseYou've already chosen the best response.4
Aha that's an interesting fact :)
 2 years ago

shegBest ResponseYou've already chosen the best response.2
yeah just google out Aswath Damodaran he is real gem.......m dying to meet this finance wizard
 2 years ago

barboatBest ResponseYou've already chosen the best response.0
mm for the 1+8+27+64+...+1000 series, we can use the Tn=a+(n1)d formula to find the top number ? but the common difference isnt the same.
 2 years ago
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