數(shù)列經(jīng)典例題(裂項(xiàng)相消法)

1、數(shù)列裂項(xiàng)相消求和的典型題型數(shù)列裂項(xiàng)相消求和的典型題型1已知等差數(shù)列的前n項(xiàng)和為則數(shù)列的前100項(xiàng)和為()na15555??SaSn11?nnaaABCD10010199101991001011002數(shù)列其前項(xiàng)之和為則在平面直角坐標(biāo)系中，直線在y軸上的截距)1(1??nnann1090)1(????nyxn為()A－10B－9C10D93等比數(shù)列的各項(xiàng)均為正數(shù)，且na6223219132aaaaa???(Ⅰ)求數(shù)列的通項(xiàng)公式；na(Ⅱ)設(shè)

2、求數(shù)列的前項(xiàng)和logloglog32313nnaaab?????1nbn4正項(xiàng)數(shù)列滿足na02)12(2????nanann(Ⅰ)求數(shù)列的通項(xiàng)公式；nana(Ⅱ)令求數(shù)列的前項(xiàng)和)1(1nnanb??nbnnT5設(shè)等差數(shù)列的前項(xiàng)和為，且nannS124224???nnaaSS(Ⅰ)求數(shù)列的通項(xiàng)公式；na(Ⅱ)設(shè)數(shù)列滿足求的前項(xiàng)和nb2112211Nnabababnnn???????nbnnT6已知等差數(shù)列滿足：的前項(xiàng)和為na267753

3、???aaanannS(Ⅰ)求及；nanS(Ⅱ)令求數(shù)列的前項(xiàng)和)(112Nnabnn???nbnnT7在數(shù)列中nannanaa211)11(21????(Ⅰ)求的通項(xiàng)公式；na(Ⅱ)令求數(shù)列的前項(xiàng)和；211nnnaab???nbnnS（Ⅱ）bn=…=﹣（12…n）=﹣，故=﹣=﹣2（﹣）則…=﹣2[（1﹣）（﹣）…（﹣）]=﹣，∴數(shù)列的前n項(xiàng)和為﹣4解：(Ⅰ)由正項(xiàng)數(shù)列an滿足：﹣（2n﹣1）an﹣2n=0，可有（an﹣2n）（an1