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# Sum to infinity of an arithmetic progression

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1. 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.
2. What's the series?
3. It's a longer series. The exact series doesn't really matter.

Sigma[n=0, ∞]En = lim[T-->∞]Sigma[n=0, T]En

And then solve for the limit?
4. Surely arithmetic series diverge?
5. (Original post by 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.
6. (Original post by 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

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