=lim1=0, n-nn n→》+0 f(x)=x-Ix(x>0), f'(x)=1->0(x>1,∴在(1,+∞)上单增, 1 即 单减,故 1当n>1时单减 n-Inn =Ln+1(n>1), n-Inn (n+1)-In(n+1) 所以此交错级数收敛,故原级数是条件收敛0, ln 1 1 lim ln 1 lim = − = − →+ →+ n n n n n n n f (x) = x − ln x (x 0), 0 ( 1), 1 ( ) = 1− x x f x 在 (1,+) 上单增, , ln 1 即 单减 x − x 1 , ln 1 故 当 时单减 − n n n ( 1), ( 1) ln( 1) 1 ln 1 = 1 + − + − = u + n n n n n u n n 所以此交错级数收敛,故原级数是条件收敛.