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3log 2 +(1)/(4) -(1)/(2)((1)/(4))^(2)+(1...

`3log 2 +(1)/(4) -(1)/(2)((1)/(4))^(2)+(1)/(3)((1)/(4))^(3)-….. = `

A

log3

B

log5

C

log 10

D

log 2

Text Solution

Verified by Experts

The correct Answer is:
C
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(1)/(1.3).(1)/(2)+(1)/(2.4).(1)/(2^(2))+(1)/(3.5).(1)/(2^(3))+....=

(1)/(2!)+(1)/(3!)+(1)/(4!)+....=

(1)/(1.2)-(1)/(2.3)+(1)/(3.4)-(1)/(4.5)+....=

A : (1)/(2)-(1)/(2).(1)/(2^(2))+(1)/(3).(1)/(2^(3))-(1)/(4).(1)/(2^(4))+....=log_(e)((3)/(2)) R : log_(e)(1+x)=x-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+...

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