# Interval of convergence

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Find the interval of convergence of (a) f(x), (b) f'(x), (c) f''(x), (d) {f(x)dx

En=1 [(-1)^n+1 (x-2)^n ] / 2

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#### Solution Preview

Solution. I guess your question is to find the interval of the series with power function term. Is the general term as follows?

Fn(x)=1/2*[(-1)^(n+1)*(x-2)^n]

I answer your question if Fn(x) is of the form above.

The series F1(x)+F2(x)+...+Fn(x)+...

=1/2*(x-2)-1/2*(x-2)^2+...+1/2*(-1)^(n+1)*(x-2)^n+...

...

#### Solution Summary

An interval of convergence is found.

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