用裂项相消法做下列3个题 1.an=1/n(n+1) 2.an=1/(3n+1)(3n+2) 3.an=1/n²+2n

问题描述:

用裂项相消法做下列3个题 1.an=1/n(n+1) 2.an=1/(3n+1)(3n+2) 3.an=1/n²+2n

an=1/[n(n+1)]=(1/n)- [1/(n+1)](裂项)

则 Sn=1-(1/2)+(1/2)-(1/3)+(1/3)-(1/4)…+(1/n)- [1/(n+1)](裂项求和)

                = 1-1/(n+1)

                = n/(n+1)

同理

  2.an=1/(3n+1)(3n+2)=[1/(3n+1)]- [1/(3n+2)]

  3.an=1/n²+2n=1/[n(n+2)]=1/2【(1/n)- [1/(n+2)]】

第二个和第三个能把列项求和步骤写出来吗?谢谢!