等差数列{a}中,前三项分别为x,2x,5x-4,前n项和为Sn,且Sk=20.（1）求x和k的值（2）求和：Tn=3/S1+3/S2
问题描述：
等差数列{a}中,前三项分别为x,2x,5x-4,前n项和为Sn,且Sk=20.（1）求x和k的值（2）求和：Tn=3/S1+3/S2
+3/S2+……+3/Sn
答
an = a1+(n-1)d
a1 =x
a2=2x = a1+ d
d=x
a3= 5x-4 = a1+2d
5x-4= x+ 2x
x=2
an = 2+(n-1)2 = 2n
Sk =20
(2+2k)k/2=20
(1+k)k =20
k^2+k -20=0
(k-4)(k+5)=0
k = 4
(2)
bn = 3/Sn
= 3/[(n+1)n]
= 3[ 1/n -1/(n+1) ]
Tn=3/S1+3/S2+3/S2+……+3/Sn
= b1+b2+...+bn
= 3( 1- 1/(n+1) )
= 3n/(n+1)