等差数列{an}中,前三项分别为x,2x,5x-4,前n项和为Sn,且Sk=72.(1)求x和k的值;(2)求Tn=1S1+1S2+1S3+…+1Sn.-数学

题目简介

等差数列{an}中,前三项分别为x,2x,5x-4,前n项和为Sn,且Sk=72.(1)求x和k的值;(2)求Tn=1S1+1S2+1S3+…+1Sn.-数学

题目详情

等差数列{an}中,前三项分别为x,2x,5x-4,前n项和为Sn,且Sk=72.
(1)求x和k的值;
(2)求Tn=
1
S1
+
1
S2
+
1
S3
+…+
1
Sn
题型:解答题难度:中档来源:不详

答案

(1)由4x=x+5x-4得x=2,…(3分)
∴an=2n,Sn=n(n+1),
∵Sk=72
∴k(k+1)=72得k=8.…(6分)
(2)∵Sn=n(n+1),∴class="stub"1
Sn
=class="stub"1
n(n+1)
=class="stub"1
n
-class="stub"1
n+1
.…(9分)
T=1-class="stub"1
2
+class="stub"1
3
-class="stub"1
3
+class="stub"1
4
…class="stub"1
n-1
+class="stub"1
n
-class="stub"1
n
-class="stub"1
n+1
=1-class="stub"1
n+1
=class="stub"n
n+1
.…(12分)

更多内容推荐