1. ## Integration problem

Let, Yn= integration of {e^(-nt)}/t , from 0 to 1, where n is a natural number. what can be said about the sequence {Yn}?

Pleaze help me for this problem. at least hep me finding the integration part.

2. Umm, as far as I know, none of those integrals converge. Just to be clear, you do mean that

$\displaystyle \displaystyle Y_{n}=\int_{0}^{1}\frac{e^{-nt}}{t}\,dt,$ right?

also, please tell me what happens if the limit is from 1 to 2.

4. Well, the integral $\displaystyle \displaystyle\int_{0}^{1}\frac{1}{t}\,dt$ does not converge, and

$\displaystyle \displaystyle\int_{0}^{1}\frac{e^{-nt}}{t}\,dt\ge \int_{0}^{1}\frac{e^{-n}}{t}\,dt=e^{-n}\int_{0}^{1}\frac{1}{t}\,dt,$ assuming $\displaystyle n>0.$

So, by the comparison test, you've got yourself a divergent integral.

[EDIT] If you go with the interval [1,2], then everything in sight is suddenly convergent. But you've got not-so-nice integrals to deal with.

5. thanks a lot. and what if the limit is from 1 to 2?

6. See the edit in my previous post.

7. ya. got it. thnx.

8. You're welcome. Have a good one!