Question

設(shè)等差數(shù)列{a_n},{b_n}的前n項(xiàng)和分別為S_n,T_n,若對(duì)任意自然數(shù)n都有=,則+的值為　　　.

Answer 1

∵{a_n},{b_n}為等差數(shù)列,
∴+=+===.
∵====,∴=.
【方法技巧】巧解等差數(shù)列前n項(xiàng)和的比值問(wèn)題
關(guān)于等差數(shù)列前n項(xiàng)和的比值問(wèn)題,一般可采用前n項(xiàng)和與中間項(xiàng)的關(guān)系,尤其是項(xiàng)數(shù)為奇數(shù)時(shí)S_n=na_中,也可利用首項(xiàng)與公差的關(guān)系求解.另外,熟記以下結(jié)論對(duì)解題會(huì)有很大幫助:若數(shù)列{a_n}與{b_n}都是等差數(shù)列,且前n項(xiàng)和分別是S_n與T_n,則=.