Sum to infinity of an arithmetic progression

Ok, I'm just slightly confused.
I have to find the sum to infinity of a series, which turns out to be arithmetic in its nature. Is it correct to find the sum from n=1 to n=n, because you clearly cannot define n=infinity.

Reply 1

Square

13

What's the series?

Reply 2

tinypony

OP

It's a longer series. The exact series doesn't really matter.

How about I just write:

Sigma[n]En = lim[T-->∞]Sigma[n]En

And then solve for the limit?

Reply 3

Swayum

18

Surely arithmetic series diverge?

Reply 4

username21537

2

Siddhartha

Ok, I'm just slightly confused.
I have to find the sum to infinity of a series, which turns out to be arithmetic in its nature. Is it correct to find the sum from n=1 to n=n, because you clearly cannot define n=infinity.

You cant define n=infinity, but you can consider the limit as n tends to infinity.

Also, as aleady said, an arithmetic progression diverges since its comparable to the sum of n, which is divergent. The "sum to infinity" is only really heard of in geometric series' in my experience.

Reply 5

DFranklin

18

mr_jr

`in my experience.

That's probably because you don't have much experience of convergent series other than geometric ones.

But you can use "sum to infinity" for any series that converges; for example $\sum_1^\infty \frac{1}{n(n+1)} = 1$

Reply 6

Baeha

Original post

by DFranklin

That's probably because you don't have much experience of convergent series other than geometric ones.

But you can use "sum to infinity" for any series that converges; for example $\sum_1^\infty \frac{1}{n(n+1)} = 1$

Sorry can someone explain this further