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(1)/(3)+(1)/(3.3^(3))+(1)/(5.3^(5))+(1)/...

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

A

log 2

B

`(1)/(2)` log 2

C

2 log 2

D

log `(1//2)`

Text Solution

Verified by Experts

The correct Answer is:
B
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(1)/(5)+(1)/(3.5^(3))+(1)/(5.5^(5))+(1)/(7.5^(7))+....=

Assertion (A) : (1)/(5)+(1)/(3.5^(3))+(1)/(5.5^(5))+(1)/(7.5^(7))+…(1)/(2)log((3)/(2)) Reason (R ) : If |x| lt 1 then log_(e )((1+x)/(1-x))=2(x+(x^(3))/(3)+(x^(5))/(5)+…)

x=(1)/(3)+(1)/(3.3^(3))+(1)/(5.3^(5))+….. y=(1)/(5)+(1)/(3.5^(3))+(1)/(5.5^(5))+…. z=1+(1)/(3.2^(2))+(1)/(5.2^(4))+(1)/(7.2^(6))+….. Then descending order of x, y, z

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))+....=

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

(1)/(2.3)+(1)/(4.5)+(1)/(6.7)+……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)/(1.3)+(1)/(2.5)+(1)/(3.7)+(1)/(4.9)+...=