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stukbv
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Homework Statement
Sum 1/n(n+1) * (sin(x))^n .
Show this converges for all x in the reals.
Find with proof an interval on which it determines a differentiable function of x together with an expression of its derivative in terms of standard functions.
Homework Equations
The Attempt at a Solution
I have showen convergence via a comparison to sum 1/n(n+1) so this is okay,
I think now we let x=sinx and write it like ;
Sum 1/n(n+1) * x^n .
Differentiating this gives you 1/(n+1) * x^n-1 now basically am stuck again :(
Thankyou!