直接Taylor展开，取有限项：sin(1/n) ~ 1/n - (1/n)^3/3!ln(1-1/n) ~ -1/n - (1/n)^2/2sin(1/n) - kln(1-1/n) = (1/n)(1+k) - (1/n)^3/3! + k[1/n + (1/n)^2/2]因为调和级数{1/n}发散，若要此级数收敛，则 1+k = 0。得， k = -1
