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.
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.
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.