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Statement-I : (1)/(1.2)+(1)/(2.2^(2))+(1...

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

A

Only I

B

Only II

C

both I & II

D

neither I nor II

Text Solution

Verified by Experts

The correct Answer is:
D
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AAKASH SERIES-LOGARITHMIC SERIES -EXERCISE - II(B) (HOME WORK)
  1. y=(x^(3)+(x^(6))/(2)+(x^(9))/(3)+……) then

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  2. If |x|lt 1, tnen the coefficient of x^(5) in the expansion of (1-x)log...

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  3. (1)/(3)+(1)/(2.3^(2))+(1)/(3.3^(3))+(1)/(4.3^(4))+….oo=

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

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  5. The 3^(rd) term in log((1)/(1-x)) is

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

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  7. 2log x-log(x+1)-log(x-1)=

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  8. If x^(2)y=2x-y then y^(2)+(y^(4))/(2)+(y^(6))/(3)+…oo=

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  9. If higher powers of x^(2) are neglected, then the value of log(1+x^(2)...

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  10. If (1)/(n+1)+(1)/(2(n+1)^(2))+(1)/(3(n+1)^(3))+….= lambda((1)/(n)-(1...

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  11. Assertion (A) : coefficient x^(n) in log(1+x) is ((-1)^(n-1))/(n) when...

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  12. Observe the following lists. {:("LIST - I","LIST - II"),((A) 8^(th)"...

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  13. x+(x^(3))/(3)+(x^(5))/(5)+(x^(7))/(7)+….oo=

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  14. 2[7^(-1)+3^(-1)7^(-3)+5^(-1)7^(-5)+…]=

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  15. 2[(1)/(2x+1)+(1)/(3*(2x+1)^(3))+(1)/(5*(2x+1)^(5))+…..oo]=

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  16. (2x)/(x^(2)+1)+(1)/(3)((2x)/(x^(2)+1))^(3) +(1)/(5)((2x)/(x^(2)+1))^(5...

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  17. x=(1)/(3)+(1)/(3.3^(3))+(1)/(5.3^(5))+….. y=(1)/(5)+(1)/(3.5^(3))+(1...

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  18. If f(x)=1+x^(2)+x^(4)+x^(6)+…..oo then int(0)^(x)f(x)dx=

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  19. Statement-I : (1)/(1.2)+(1)/(2.2^(2))+(1)/(3.2^(3))+….oo=log(e )1//2 ...

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  20. Assertion (A) : (1)/(5)+(1)/(3.5^(3))+(1)/(5.5^(5))+(1)/(7.5^(7))+…(1)...

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