数学求级数和,∑(n=1,∝)x^n-1/n2^n

Question

数学求级数和,
∑(n=1,∝)x^n-1/n2^n

Answer 1

级数收敛域为[-2,2).设和函数为S(x),则xS(x)=∑(n=1,∝)x^n/n2^n,两端求导,得[s(x)]'=1/(2-x)上式对x积分：上限x,下限0.则xS(x)=-ln(2-x)+ln2x≠0时,S(x)=-(1/x)ln[(1-x)/2)]x=0时,S(x)=1/2解题思路：先求收敛域,确...