证明级数收敛性,求和.请不要省略步骤,新手,谢谢.

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证明级数收敛性,求和.请不要省略步骤,新手,谢谢.

证明级数收敛性,求和.请不要省略步骤,新手,谢谢.
证明级数收敛性,求和.
请不要省略步骤,新手,谢谢.

证明级数收敛性,求和.请不要省略步骤,新手,谢谢.
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...

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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

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