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[{((1)/(3))^(-3)-((1)/(2))^(-3)}-:((1)/(...

`[{((1)/(3))^(-3)-((1)/(2))^(-3)}-:((1)/(5))^(-2)]`

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I:2[((1)/(3))+(1)/(3)((1)/(3))^(3)+(1)/(5)((1)/(3))^(5)+...]=log_(e)2 II:2[((1)/(2))+(1)/(3)((1)/(2))^(3)+(1)/(5)((1)/(2))^(5)+...]=log_(e)2

2[((1)/(2))+(1)/(3)((1)/(2))^(3)+(1)/(5)((1)/(2))^(5)+...]=

2[((1)/(3))+(1)/(3)((1)/(3))^(3)+(1)/(5)((1)/(3))^(5)+...] =

2[((2)/(3))+(1)/(3)((2)/(3))^(3)+(1)/(5)((2)/(3))^(5)+...]=

(-(1)/(2)-(2)/(3)+(4)/(5)-(1)/(3)+(1)/(5)+(3)/(4))/((1)/(2)+(2)/(3)-(4)/(3)+(1)/(3)-(1)/(5)-(4)/(5)) is simplified to

e^(2((1)/(3)+(1)/(3)*(1)/(3^(3))+(1)/(5)*(1)/(3^(5))+….))=

e^(2((1)/(3)+(1)/(3)*(1)/(3^(3))+(1)/(5)*(1)/(3^(5))+….))=

The sum of (1)/(2)+(1)/(3)*((1)/(2^(3)))+(1)/(5)*((1)/(2^(5)))+....oo is

1+((1)/(2)+(1)/(3))/((1)/(3)-(1)/(6))/2-((4)/(5)of(5)/(6))/((2)/(3))