What is the interval of convergence of $sum_1^oo ((-1)^(n-1)*x^(n+1))/((n+1)!)$ ?

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Answer 1 · 2018-04-30T18:05:32

Use the ratio test to detmeurine the radius of convergence first:

$L = lim_(n-> oo) (((-1)^(n)x^(n + 2))/((n + 2)!))/(((-1)^(n - 1)x^(n + 1))/((n + 1)!)$

$L = lim_(n->oo) (-1(x))/(n + 2)$

Take the absolute value.

$L = |x|lim_(n->oo) 1/(n + 2)$

$L = |x| (0)$

$L = 0$

This converges for all values of $x$ , because the ratio test came back between $0$ and $1$ .

The interval of convergence is therefore $(-oo, oo)$ .

Hopefully this helps!

What is the interval of convergence of sum_1^oo ((-1)^(n-1)*x^(n+1))/((n+1)!)sum_1^oo ((-1)^(n-1)*x^(n+1))/((n+1)!)?