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Infinite? and how to demostrate it?

which progression is the sequence in ?

I cant find any order...

each term is just the sum of '1st n natural numbers'

which is n(n+1)/2

thats your general term \(a_n =n(n+1)/2\)

how do you find whether next sequence has a limit ?

Why is that the general term?

a1=1(1+1)/2=2/2=1 Does not apply...

1st term is indeed 1 right ?
1, 1+2 , 1+2+3 , ....
1,3,6, 10,...

Oh...now I understand! Give me a minute

So:
2Sn= (n+1) + (n+2) + (n+4)...ehm...this is not going right

so you want to find the sum ?

\(\Large (1/2)\sum (n^2+n) = (1/2)\sum n^2+(1/2)\sum n=...?\)

Oh...I thought that I could add Sn + Sn, and then divide them by two to get the general term

possible but i don't think its that easy....

then how to get the limit?

When it says "the next sequence" it refers to the one I put

ok, so you just want to find whether the sum converges or not ?

What means converges?

sum converge means sum = finite

yes, it is infinite

Thanks :)

How did you wrote the general term? Is there a mathematical way to get it?

so, sum of 1st n natural numbers = n (n+1)/2

sorry for the typos :P

Thanks for a lot

welcome ^_^

that is an =

ok, let me try

but I dont have a1

yes, i though it was already given....

nope :/

So can it be determined with the things given?

i am not sure about this....can you ask in new post so that others can try.....sorry.