Sn=2+4+6+…+2n,则1/S1+1/S2+1/S3+…1/SN的值为_数学解答

Sn=2+4+6+…+2n,则1/S1+1/S2+1/S3+…1/SN的值为

人气：394 ℃　时间：2020-05-13 13:29:26

解答

Sn=2+4+6+…+2n = 2* [1+2+...+n] = 2*n(n+1)/2 = n(n+1)
1/sn = 1/n(n+1) = 1/n - 1/(n+1)
1/S1+1/S2+1/S3+…1/SN
=[1-1/2]+[1/2-1/3]+[1/3-1/4]+...+[1/(N-1)-1/N]+[1/N-1/(N+1)]
= 1-1/(N+1)
= N/(N+1)