Question

【題目】【2017遼寧葫蘆島市二模】已知數(shù)列滿足： .

（1）求數(shù)列的通項(xiàng)公式；

（2）若,求數(shù)列的前項(xiàng)和.

Answer 1

【答案】見(jiàn)解析

【解析】(1)當(dāng)n=1時(shí),a1=4-=1.

當(dāng)n≥2時(shí),

a1+2a2+…+nan=4-..........................①

a1+2a2+…+(n-1)an=4-..........................②

①-②得: nan=-= (2n+2-n-2)=

an=

當(dāng)n=1時(shí),a1也適合上式, ∴an= (nN*).

(2) bn=(3n-2)

Sn=+++…+(3n-5) +(3n-2) ......................①

Sn=+++…+(3n-5) +(3n-2) ......................②

①-②得: Sn=+3(+++…+)-(3n-2) =1+-(3n-2)

解得:Sn=8-.