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(1)/(2)((1)/(5)+(1)/(7))-(1)/(4)((1)/(5^...

`(1)/(2)((1)/(5)+(1)/(7))-(1)/(4)((1)/(5^(2))+(1)/(7^(2)))+(1)/(6)((1)/(5^(3))+(1)/(7^(3)))-….oo=`

A

`(1)/(2)log_(e )(5//7)`

B

`(1)/(2)log_(e )(47//35)`

C

`log_(e )(47//35)`

D

`log_(e )(35//47)`

Text Solution

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The correct Answer is:
B
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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

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

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

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

(1)/(2.3)+(1)/(4.5)+(1)/(6.7)+(1)/(8.9)+...

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

1+(1)/(3.2^(2))+(1)/(5.2^(4))+(1)/(7.2^(6))+....=

(1)/(2)+(3)/(2).(1)/(4)+(5)/(3).(1)/(8)+(7)/(4).(1)/(16)+....=

AAKASH SERIES-LOGARITHMIC SERIES -EXERCISE - II(A) (CLASS WORK)
  1. If y=x+(x^(2))/(2)+(x^(3))/(3)+....oo, then x =

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  2. If f(x)=1-x+x^(2)-x^(3)+x^(4)+….oo then int(0)^(x)f(x)dx=

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  3. (1)/(2)((1)/(5)+(1)/(7))-(1)/(4)((1)/(5^(2))+(1)/(7^(2)))+(1)/(6)((1)/...

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  4. If alpha, beta are the roots of x^(2)-px+q=0 then (alpha+beta)x-(alp...

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  5. n^(th) term of log(e )(6//5) is

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  6. log(4)2-log(8)2+log(16)2-....=

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  7. 2.4^((-1)/(4))*8^((1)/(9))*16^((-1)/(16))*32^((1)/(25))*64^((-1)/(36))...

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  8. (1)/(1.2)-(1)/(2.3)+(1)/(3.4)-(1)/(4.5)+....=

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  9. (4)/(1.3)-(6)/(2.4)+(12)/(5.7)-(14)/(6.8)+….=

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  10. (1)/(1.3)+(1)/(2.5)+(1)/(3.7)+(1)/(4.9)+...=

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  11. The 3^(rd), 4^(th), 5^(th) terms in the expansion of log(e )2 are resp...

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  12. sum(n=1)^(oo)(1)/(2n(2n+1))=

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  13. -2[(1)/(8)+(1)/(64)+(1)/(384)+…..oo]=

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  14. If |x| lt 1 then coefficient of x^(n) in log(10)(1-x) is

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  15. log(1+x+x^(2)+...oo)=

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  16. (2)/(1).(1)/(3)+(3)/(2).(1)/(9)+(4)/(3).(1)/(27)+(5)/(4).(1)/(81)+…oo=

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  17. (sqrt(2)-1)/(sqrt(2))+(3-2sqrt(2))/(4)+(5sqrt(2)-7)/(6sqrt(2))+……oo=

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  18. Assertion (A) : If x+(x^(2))/(2)+(x^(3))/(3)+………oo=log((7)/(6)) then...

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  19. If f(x)=(1)/(x+1)+(1)/(2(x+1)^(2))+(1)/(3(x+1)^(3))+…(x gt 1) and f(1...

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  20. y=2x^(2)-1, then (1)/(x^(2))+(1)/(2x^(4))+(1)/(3x^(6))+…….oo

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