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सिद्ध कीजिए की "log"(e)4/e=1/1.2-1/2.3+1...

सिद्ध कीजिए की `"log"_(e)4/e=1/1.2-1/2.3+1/3.4-1/4.5 +...oo` पद तक

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I:(1)/(1.2)+(1)/(3.4)+(1)/(5.6)+....log_(e)2 II:(1)/(1.2)-(1)/(2.3)+(1)/(3.4)-(1)/(4.5)+....=2log_(e)2-1

Prove that, 1/(1.2)-1/(2.3)+1/(3.4)-.....=2log_e2-1

Show that, log_e2=1/(1.2)+1/(3.4)+1/(5.6)+.....infty

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

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(1/(1!) +1/(2!) +1/(3!) + .....oo) (1/(2!) -1/(3!) +1/(4!)-1/(5!) .....oo)

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