证明级数收敛性，求和。

我把解答过程截图了，见下

T=∑(1到无穷）（2n-1）/3^n
3T=∑（1到无穷）（2n-1）/3^(n-1)
=∑（0到无穷）（2n+1）/3^n
=T+2∑（0到无穷）1/3^n
=T+2*1/(1-1/3)
=T+3

so T=3/2

S=∑(1到无穷）1/[n(n+1)(n+2)]
=∑(1到无穷）{1/[n(n+1]-1/[(n+1)(n+2)]}/3
=lim(n到无穷）{1/2-1/[(n+1)(n+2)]}/3
=1/6