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The sum of series (1)/(1.2) -(1)/(2....

The sum of series
` (1)/(1.2) -(1)/(2.3) + (1)/(3.4) - (1)/(4.5) + …….` is

A

`log_(e)((4)/(e ))`

B

`(4)/(e )`

C

`log_(e ) ((e )/(4))`

D

`(e )/(4)`

Text Solution

Verified by Experts

The correct Answer is:
b
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OBJECTIVE RD SHARMA ENGLISH-EXPONENTIAL AND LOGARITHMIC SERIES-Exercise
  1. If y=2x^(2)-1 then (1)/(x^(2))+(1)/(2x^(4))+(1)/(3x^(6))+…infty equals...

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  2. The sum of sum(n=1)^(oo) ""^(n)C(2) . (3^(n-2))/(n!) equal

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  3. If (e^(x))/(1-x) = B(0) +B(1)x+B(2)x^(2)+...+B(n)x^(n)+... , then the ...

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  4. IfS=Sigma(n=1)^(oo) (""^(n)C(0)+""^(n)C(1)+""^(n)c(2)+..+""^(n)C(n))/(...

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  5. If S=sum(n=2)^(oo) (3n^2+1)/((n^2-1)^3) then 9/4Sequals

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  6. 1/(1.2)+(1.3)/(1.2.3.4)+(1.3.5)/(1.2.3.4.5.6)+.....oo

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  7. The sum of the series (12)/(2!)+(28)/(3!)+(50)/(4!)+(78)/(5!)+…is

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  8. If a=Sigma(n=0)^(oo) (x^(3x))/(3n)!,b=Sigma(n=1)^(oo)(x^(3n-2))/(3n-2!...

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  9. If S(n) denotes the sum of the products of the products of the first n...

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  10. sum(n=0)^oo (loge x)^n/(n!) is equal to

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  11. If a = Sigma(n=1)^(oo) (2n)/(2n-1!),b=Sigma(n=1)^(oo) (2n)/(2n+1!) the...

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  12. The value of (1+(a^(2)x^(2))/(2!)+(a^(4)x^(4))/(4!)+…)^(2)-(ax+(a^(3...

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  13. If S(n)=(1^(2).(2))/(1!)+(2^(2).3)/(2!)+(3^(2).4)/(3!)+…(n^(2).(n+1))...

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  14. If S=Sigma(n=0)^(oo) (logx)^(2n)/(2n!) , then S equals

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  15. If y+(y^(3))/(3)+(Y^(5))/(5)+…infty=2(x+(x^(3))/(3)+(x^(5))/(5)+..inft...

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  16. The value of log 2+2 (1/5+1/3.(1)/(5^(3))+1/5.(1)/(5^(5))+..+infty) is

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  17. The sum of series (1)/(1.2) -(1)/(2.3) + (1)/(3.4) - (1)/(4.5) + …...

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  18. e^{(x-1)-1/2(x-1)^2+((x-1)^3)/3-(x-1)^(4)/4+......} is eqaul to

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  19. 2{(m-n)/(m+n)+1/3((m-n)/(m+n))^(3)+1/5((m-n)/(m+n))^(5)+..} is equals ...

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  20. log4 2-log8 2+log16 2-.....oo

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