对已知级数 1/(1 - x) = ∑(n=1~inf.)x^(n-1),|x| < 1,两端积分,得 -ln|1-x| = ∫[0, x][∑(n=1~inf.)t^(n-1)]dt = ∑(n=1~inf.)∫[0, x][t^(n-1)]dt = ∑(n=1~inf.)[(x^n)/n] ,-1 <= x < 1,……。