Question

幂级数∑x^n/n*2^n 的收敛半径

Answer 1

[x^(n+1)/(n+1)*2^(n+1)]/[x^n/n*2^n]
=nx/2(n+1)
当n→∞,|nx/2(n+1)|＜1
即|x|＜2
即幂级数∑x^n/n*2^n 的收敛半径为2.