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

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

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

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

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

FoolForMath
 3 years ago
Best 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.

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

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

FoolForMath
 3 years ago
Best ResponseYou've already chosen the best response.4Fool 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 ;)

sheg
 3 years ago
Best ResponseYou've already chosen the best response.2bottom 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

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

FoolForMath
 3 years ago
Best ResponseYou've already chosen the best response.410 is the number of terms or number of iterations

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

barboat
 3 years ago
Best ResponseYou've already chosen the best response.0for 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 ?

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

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

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

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

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

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

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

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

AditiMeow
 3 years ago
Best ResponseYou've already chosen the best response.0Sorry n =1 at the bottom

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

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

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

FoolForMath
 3 years ago
Best ResponseYou've already chosen the best response.4aditi you know about arithmetic progression ?

sheg
 3 years ago
Best ResponseYou've already chosen the best response.2and 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

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

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

FoolForMath
 3 years ago
Best ResponseYou've already chosen the best response.4No it is the number of iteration

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

AditiMeow
 3 years ago
Best ResponseYou've already chosen the best response.0WOW I dont Know Maths =D

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

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

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

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

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

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

AditiMeow
 3 years ago
Best ResponseYou've already chosen the best response.0I learnt AP without Sigma

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

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

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

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

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

FoolForMath
 3 years ago
Best ResponseYou've already chosen the best response.4but 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 :)

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

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

AditiMeow
 3 years ago
Best ResponseYou've already chosen the best response.0i understood the question barboat asked =)

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

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

sheg
 3 years ago
Best 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

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

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

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

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

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

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

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

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

sheg
 3 years ago
Best ResponseYou've already chosen the best response.2i 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

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

sheg
 3 years ago
Best ResponseYou've already chosen the best response.2yeah 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

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

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

barboat
 3 years ago
Best ResponseYou've already chosen the best response.0mm 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.
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