已知数列{1an}是公差为2的等差数列,且a1=1.(1)求数列{an}的通项公式; (2)求数列{an?an+1}的前n项

2025-05-12 13:01:48
推荐回答(1个)
回答(1):

(1)∵数列{

1
an
}是公差为2的等差数列,且a1=1.
1
an
=1+2(n-1),解得an=
1
2n?1

(2)∵an?an+1=
1
(2n?1)(2n+1)
=
1
2
(
1
2n?1
?
1
2n+1
)

∴数列{an?an+1}的前n项和Tn=
1
2
[(1?
1
3
)+(
1
3
?
1
5
)+
…+(
1
2n?1
?
1
2n+1
)]

=
1
2
(1?
1
2n+1
)

=
n
2n+1