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(1)/(1.3)+(1)/(3.5)+(1)/(5.7)+......

(1)/(1.3)+(1)/(3.5)+(1)/(5.7)+...

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The sum of the series (1)/(1.3.5)+(1)/(3.5.7)+(1)/(5.7.9)+... is

(1)/(1.3)+(1)/(2)((1)/(3.5))+(1)/(3)((1)/(5.7))+....=

(1)/(1.2.3)+(1)/(3.4.5)+(1)/(5.6.7)+....

(1)/(1.2.3)+(1)/(3.4.5)+(1)/(5.6.7)+....

(1)/(1.3.5)+(1)/(3.5.7)+...

(1)/(1.3.5)+(1)/(3.5.7)+

The sum to n terms of [(1)/(1.3)+(2)/(1.3.5)+(3)/(1.3.5.7)+(4)/(1.3.5.7.9)+…………]

The sum to n terms of [(1)/(1.3)+(2)/(13.5)+(3)/(1.3.5.7)+(4)/(1.3.5.7.9)+…………]