⑩天掌 Teaching Plan on Advanced Mathematics 显然xm+1>xn,{xn}是单调递增的; x.<1+1++…+-<1+1+-+…+ 2 3 2n13 {xn}是有界的; ∴ limx存在 n→0l 记为lm(1+)”=e(e=271828) n→》Q 可以证明, im(1+-)2=lim(1+-)=e n1→+0 n→Tianjin Polytechnic University Teaching Plan on Advanced Mathematics , 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 3 2 1 3 1 = −  n−  是有界的;  x n lim 存在. n n x →  e n n n + = → ) 1 记为lim(1 (e = 2.71828) 可以证明, e x x x n x n + = + = →+  →−  ) 1 ) lim (1 1 lim (1