高一数学求解(详细过程）

已知等差数列前三项为a,4,3a，前n项和为Sn,Sm=2550
(1)求a和m的值
(2)求1/S +1/S2 +......+1/Sn

a+3a=4*2

a=2

d=4-2=2
an=2+2(n-1)

Sm=[2+2+2(m-1)]*m/2=2550

(m+1)m=2550

(m+51)(m-50)=0

m=-51(舍去）

m=50

2)

Sn=[2+2+2(n-1)]*n/2=n(n+1)

1/S +1/S2 +......+1/Sn

=1/1*2+1/2*3+....+1/n(n+1)

=1-1/2+1/2-1/3+...+1/n-1/(n+1)

=1-1/(n+1)

=n/(n+1)