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osanseviero
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Is there a limit in this progression? 1.1 + 2.1 + 2 + 3.1 + 2 + 3 + 4
 11 months ago
 11 months ago
osanseviero Group Title
Is there a limit in this progression? 1.1 + 2.1 + 2 + 3.1 + 2 + 3 + 4
 11 months ago
 11 months ago

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osanseviero Group TitleBest ResponseYou've already chosen the best response.1
Infinite? and how to demostrate it?
 11 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
which progression is the sequence in ?
 11 months ago

osanseviero Group TitleBest ResponseYou've already chosen the best response.1
The question: 1. Determine if the next sequence has a limit (demostrate it) and determine it (hint:find the general term) c) 1,1 + 2,1 + 2 + 3,1 + 2 + 3, + 4...
 11 months ago

osanseviero Group TitleBest ResponseYou've already chosen the best response.1
I cant find any order...
 11 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
each term is just the sum of '1st n natural numbers'
 11 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
which is n(n+1)/2
 11 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
thats your general term \(a_n =n(n+1)/2\)
 11 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
how do you find whether next sequence has a limit ?
 11 months ago

osanseviero Group TitleBest ResponseYou've already chosen the best response.1
Why is that the general term?
 11 months ago

osanseviero Group TitleBest ResponseYou've already chosen the best response.1
a1=1(1+1)/2=2/2=1 Does not apply...
 11 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
1st term is indeed 1 right ? 1, 1+2 , 1+2+3 , .... 1,3,6, 10,...
 11 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
and each term is sum of 1st n natural numbers 1st term = 1 2nd term = sum of 1st 2 natural numbers =1+2 =3 and so on
 11 months ago

osanseviero Group TitleBest ResponseYou've already chosen the best response.1
Oh...now I understand! Give me a minute
 11 months ago

osanseviero Group TitleBest ResponseYou've already chosen the best response.1
Cant you add the series plus iteslf? like this: Sn= 1 + 3 + 6 + 10 + ... + n2 + n1 + n Sn= n + n1 + n2 +...+ 6 + 3 + 1
 11 months ago

osanseviero Group TitleBest ResponseYou've already chosen the best response.1
So: 2Sn= (n+1) + (n+2) + (n+4)...ehm...this is not going right
 11 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
so you want to find the sum ?
 11 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
\(\Large (1/2)\sum (n^2+n) = (1/2)\sum n^2+(1/2)\sum n=...?\)
 11 months ago

osanseviero Group TitleBest ResponseYou've already chosen the best response.1
Oh...I thought that I could add Sn + Sn, and then divide them by two to get the general term
 11 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
possible but i don't think its that easy....
 11 months ago

osanseviero Group TitleBest ResponseYou've already chosen the best response.1
then how to get the limit?
 11 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
how do you find whether next sequence has a limit ? i may know it, but not in these "limit of next sequence" terms ...
 11 months ago

osanseviero Group TitleBest ResponseYou've already chosen the best response.1
When it says "the next sequence" it refers to the one I put
 11 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
ok, so you just want to find whether the sum converges or not ?
 11 months ago

osanseviero Group TitleBest ResponseYou've already chosen the best response.1
Look, I have 5 exercises 1. \[\left( 1 \right)^{n}\left( \frac{ 5n+4 }{ 2n } \right)\] For this one we saw that the 4 will be nothing in comparison so the limit without the 1n is 5/2. It has no limit because it is ocilating. 2. \[2^{1}\times2^{2}\times2^{3}...\] Because there is a negative sign, it will change, so there is no limit
 11 months ago

osanseviero Group TitleBest ResponseYou've already chosen the best response.1
What means converges?
 11 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
sum converge means sum = finite
 11 months ago

osanseviero Group TitleBest ResponseYou've already chosen the best response.1
I want to know if it has a limit and to demostrate and determine it. I think that for this infinite is the limit, am I right?
 11 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
yes, it is infinite
 11 months ago

osanseviero Group TitleBest ResponseYou've already chosen the best response.1
Thanks :)
 11 months ago

osanseviero Group TitleBest ResponseYou've already chosen the best response.1
How did you wrote the general term? Is there a mathematical way to get it?
 11 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
the sum of 1st n natural numbers ? that you can find by your method, Sn = 1+2+3+....n Sn = n+n1 +n2 +...3+2+1 2Sn = (1+n)+ (1+n) +..... so, each pair sum is (1+n) and there are n terms so, 2Sn = n (n+1)
 11 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
so, sum of 1st n natural numbers = n (n+1)/2
 11 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
that became your general term and for your sequence, you need to sum this, and whne n becomes large the sum goes on increaseing which menas this progression has no limit.
 11 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
sorry for the typos :P
 11 months ago

osanseviero Group TitleBest ResponseYou've already chosen the best response.1
Thanks for a lot
 11 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
welcome ^_^
 11 months ago

osanseviero Group TitleBest ResponseYou've already chosen the best response.1
\[an?\left\{ an=\frac{ 1 }{ 2 }\left( a _{n1} + \frac{ 10 }{ a _{n1} }\right) \right\} for n \ge2\]
 11 months ago

osanseviero Group TitleBest ResponseYou've already chosen the best response.1
that is an =
 11 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
have you solved such problems, with a (n1) , before.... because i just could think of finding, a1,a2,a3...and see whether there's any pattern...
 11 months ago

osanseviero Group TitleBest ResponseYou've already chosen the best response.1
ok, let me try
 11 months ago

osanseviero Group TitleBest ResponseYou've already chosen the best response.1
but I dont have a1
 11 months ago

osanseviero Group TitleBest ResponseYou've already chosen the best response.1
this is just telling you that the new value is the last one added by 10 divded by iteslf \[\left( a ^{2} +\frac{ 10 }{ a ^{2} }\right)\] divided by two
 11 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
yes, i though it was already given....
 11 months ago

osanseviero Group TitleBest ResponseYou've already chosen the best response.1
nope :/
 11 months ago

osanseviero Group TitleBest ResponseYou've already chosen the best response.1
So can it be determined with the things given?
 11 months ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
i am not sure about this....can you ask in new post so that others can try.....sorry.
 11 months ago
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