# Math Help - Improper Integrals

1. Originally Posted by Mathstud28
ok $\int_0^{1}\frac{cos(x)}{x^2}dx=\int_0^{1}\sum_{n=1 }^{\infty}\frac{(-1)^{n}x^{2n-2}}{(2n)!}dx=\sum_{n=0}^{\infty}\frac{(-1)^{n}x^{2n-1}}{(2n-1)\cdot{(2n)!}}$ which converges from 0 to 1
But that's not the right series, did you read what TheEmptySet said?

2. Originally Posted by PaulRS
But that's not the right series, did you read what TheEmptySet said?
Yes it is $\frac{cos(x)}{x^2}=\frac{\sum_{n=0}^{\infty}\frac{ (-1)^{n}x^{2n}}{(2n)!}}{x^2}=\sum_{n=1}^{\infty}\fra c{(-1)^{n}x^{2n-2}}{(2n)!}$

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