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If log(e )k=2[(3)/(5)+(1)/(3)((3)/(5))^(...

If `log_(e )k=2[(3)/(5)+(1)/(3)((3)/(5))^(3)+(1)/(5)((3)/(5))^(5)+….oo]` then k =

A

2

B

3

C

4

D

8

Text Solution

Verified by Experts

The correct Answer is:
C
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2[((1)/(3))+(1)/(3)((1)/(3))^(3)+(1)/(5)((1)/(3))^(5)+...] =

(1)/(4)+(1)/(3)((1)/(4))^(3)+(1)/(5)((1)/(4))^(5)+…..oo=…….

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

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

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

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

log2+2[(1)/(5)+(1)/(3.5^(3))+(1)/(5.5^(5))+….oo]=

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

If (3)/(4)+(1)/(3)((3)/(4))^(3)+(1)/(5)((3)/(4))^(5)+....=log_(e)a,(1)/(3)+(1)/(3.3^(3))+(1)/(5.3^(5))+(1)/(7.3^(7))+....=log_(e)b, 1+(1)/(3.2^(2))+(1)/(5.2^(4))+(1)/(7.2^(6))+....=log_(e)c then the ascending order of a, b, c is