类似地,x1=1+1+1(-1)+ n 2 n +(1-—,)(1 )…(1 n+1n+2 n+1 2 n (n+1)!n+1n+2 n 显然xn+1>xn,∴{xn}是单调递增的; x,<1+1++…+<1+1++…+ 2! nI 2 2 =3 n1<3,{x》}是有界的; 2 .imxn存在.记为im(1+)”=e(e=271828…) n→ n→0 nn 王页下). 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    , 显然 xn+1  xn  是单调递增的;  x n ! 1 2! 1 1 1 n xn  + + ++ 1 2 1 2 1 1 1 −  + + + +  n 1 2 1 3 − = − n  3,  是有界的;  x n lim 存在. n n x →  e n n n + = → ) 1 记为lim(1 (e = 2.71828) 类似地