im(1+ x→0 设xn=(1+ n(n 1+一·-+ (n-1)…(n-n+1)1 ∴十 n 1+1+,(1--)+…+,(1--)(1--)…(1 n n+1 1+1+(1 ∴十 (1 2!n+1 n n+2(、你 n 2 (n+1)!n+ n+2 n+1二 e x x x + = → ) 1 lim(1 n n n x ) 1 设 = (1 +  + − = +  + 2 1 2! 1 ( 1) 1! 1 n n n n n ). 1 ) (1 2 )(1 1 (1 ! 1 ) 1 (1 2! 1 1 1 n n n n n n − = + + − ++ − −  − n n n n n n n 1 ! ( 1) ( 1)  − − + +  ). 1 ) (1 2 2 )(1 1 1 (1 ( 1)! 1 ) 1 1 ) (1 2 2 )(1 1 1 (1 ! 1 ) 1 1 (1 2! 1 1 1 1 + − + − + − + + + − − + − + + + − + = + + − + n n n n n n n n n n n xn   