Question

求幂级数∑(((-1)^n)/2n+1)*x^(2n+1)的收敛域及和函数,

Answer 1

收敛域是[-1,1]

f(x)=∑(((-1)^n)/2n+1)*x^(2n+1)

f'(x)=∑(((-1)^n)x^(2n)(等比数列-x^2为公比)=1/(1+x^2)

f(x)=1/(1+x^2)在(0,x)的积分=arctanx