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

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

A

2

B

4

C

1

D

3

Text Solution

Verified by Experts

The correct Answer is:
A
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Explore conceptually related problems

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

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

(1)/(3)+(1)/(3.3^(3))+(1)/(5.3^(5))+(1)/(7.3^(7))+....=

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

2[(1)/(2x+1)+(1)/(3*(2x+1)^(3))+(1)/(5*(2x+1)^(5))+…..oo]=

Statement-I : (1)/(1.2)+(1)/(2.2^(2))+(1)/(3.2^(3))+….oo=log_(e )1//2 Statement-II : ((1)/(5)+(1)/(7))+(1)/(3)((1)/(5^(3))+(1)/(7^(3)))+(1)/(5)((1)/(5^(5))+(1)/(7^(5)))+….+oo=(1)/(2)log2 Which of the above is true

(1)/(2x+1)+(1)/(3)(1)/((2x+1)^(3))+(1)/(5)(1)/((2x+1)^(5))+....=

(1)/(5)+(1)/(3.5^(3))+(1)/(5.5^(5))+(1)/(7.5^(7))+....=

(1)/(2x-1)+(1)/(3).(1)/((2x-1)^(3))+(1)/(5)(1)/((2x-1)^(5))+....=