算一道数列错位相减求和的题Sn=3+9/2+15/4+.+(6n-3)/2^(n-1)1/2Sn=3/2+9/4+15/8.+_数学解答

算一道数列错位相减求和的题
Sn=3+9/2+15/4+.+(6n-3)/2^(n-1)
1/2Sn=3/2+9/4+15/8.+(6n-3)/2^n
求Sn在线等急

人气：451 ℃　时间：2020-05-14 04:41:32

解答

1/2Sn=3+（9/2-3/2）+（15/4-9/4）+（21/8-15/8）+……+（(6n-3)/2^(n-1)-(6n-9)/2^(n-1)）-(6n-3)/2^n
=3+6/2+6/4+6/8+……+6/2^(n-1)-(6n-3)/2^n
=3+6(1-1/2^(n-1))-(6n-3)/2^n
=9-(6n+9)/2^n
Sn=18-(6n+9)/2^(n-1)