(1)计算：+2*2!+3*3!+……+n*n!(2)求证：k/(k+1)!=1/k!-1/(k+1)!(3)求证：1/2!+2/_数学解答

(1)计算：+2*2!+3*3!+……+n*n!(2)求证：k/(k+1)!=1/k!-1/(k+1)!(3)求证：1/2!+2/3!+n/(n+1)!...
(1)计算：+2*2!+3*3!+……+n*n!
(2)求证：k/(k+1)!=1/k!-1/(k+1)!
(3)求证：1/2!+2/3!+n/(n+1)!=1-1/(n+1)

人气：409 ℃　时间：2019-08-20 22:00:06

解答

(1)ak=k*k!=(k+1-1)k!=(k+1)!-k!1!+2*2!+3*3!+...+n*n!=1!+3!-2!+4!-3!+...+(n+1)!-n!=(n+1)!-1(2)1/k!-1/(k+1)!=1/k!-1/[(k+1)k!]=(1/k!)[1-1/(k+1)]=k/(k+1)!(3)限制长度了,提示用第二问结论.