lim求lim[1/5+2
解:
`1/5+1/5^3+1/5^5+……+1/5^(2n-1)
=1/5×(1-1/25^n)/(1-1/5^2)
=5(1-1/25^n)/24
`2/5^2+2/5^4+……+2/5^2n
=2/5^2×(1-1/25^n)/(1-1/5^2)
=(1-1/25^n)/12
所以原式=lim[5(1-1/25^n)/24+(1-1/25^n)/12] n→∞
````````=5/24+1/12=7/24。
解:
`1/5+1/5^3+1/5^5+……+1/5^(2n-1)
=1/5×(1-1/25^n)/(1-1/5^2)
=5(1-1/25^n)/24
`2/5^2+2/5^4+……+2/5^2n
=2/5^2×(1-1/25^n)/(1-1/5^2)
=(1-1/25^n)/12
所以原式=lim[5(1-1/25^n)/24+(1-1/25^n)/12] n→∞
````````=5/24+1/12=7/24。
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