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निम्नांकित श्रेणियों का योगफल निकालिए। ...

निम्नांकित श्रेणियों का योगफल निकालिए।
`1+1/3 . 1/4+1.4/3.6 . 1/4^(2)+(1.4.7)/(3.6.9) . 1/4^(3)+...oo` पदों तक

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1+1/3x+1.4/3.6 x^(2)+(1.4.7)/(3.6.9) x^(3)+…. =

(1) / (1.2) + (1.3) / (1.2.3.4) + (1.3.5) / (1.2.3.4.5.6) + .... oo

1/(1.2)+(1.3)/(1.2.3.4)+(1.3.5)/(1.2.3.4.5.6)+.....oo

Prove that (1-1/3+1/3^(2)-1/3^(3)+1/3^(4)-...oo)=3/4

Find (1)/(3)+(1)/(2.3^(2))+(1)/(3.3^(3))+(1)/(4.3^(4))+….oo=?

1+(1)/(2). (3)/(5) + (1.3)/(2.4) . (9)/(25)+(1.3.5)/(2.4.6).(27)/(125)+…...oo=