Question

已知等差数列｛an｝满足：a3=7，a5+a7=26.｛an｝的前n项和为Sn

已知等差数列｛an｝满足：a3=7，a5+a7=26.｛an｝的前n项和为Sn 1.求An及Sn；2.令Bn=1/An^2-1(n∈N*),求数列｛bn｝的前n项和Tn

Answer 1

已知数列{an}是等差数列,其前n项和为sn,a3=7,s4=24
,sn=na1
n(n-1)d,4a1
4(4-1)d=24,
a1
2d=7,d=-1,a1=9,设p、q是正整数,且p≠q,s(p
q)=9(p
q)-(p
q)(p
q-1)=10(p
q)-(p
q)²,
(s2p
s2q)/2
=[18p-2p(2p-1)
18q-2q(2q-1)]/2=10(p
q)-2(p²
q²),p²
q²>2pq,
2(p²
q²)>(p
q)²,-2(p²
q²)<-(p
q)²,10(p
q)-2(p²
q²)<10(p
q)-(p
q)²,
s(p
q)>1/2(s2p
s2q)
.