例2证明lm(1+-)存在 n→0 证明: n+1 n+I 1+ =1+(n+1) ++C n+1 n+1 n n+//+…+ n+1 n 1 1+n·-+…+C1) 十。十 k k 1)(n-1).(n-k+1) ! 2 k-1例 2 证明 存在 。 n n n ) 1 lim ( 1 + →  证明： 1 1 1 1 1 1 ... 1 1 ... 1 1 1 ( 1) 1 1 1 + + + +   +  + +   + + + +  = + +    + = + k n kn n n n n C n n n a k n kn n n n n C n n n a    + +    = +  + +   = + 1 ... 1 ... 1 1 1 1   −  −   −   = −   − − +   =   nk k n n k n n n n k n C k k kn 1 ... 1 2 1 1 1 !1 1 ! 1 ( 1)...( 1)