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If 1-1/3+1/5-1/7+1/9-1/(11)+=pi/4 , then...

If `1-1/3+1/5-1/7+1/9-1/(11)+=pi/4` , then value of `1/(1xx3)+1/(5xx7)+1/(9xx11)+` is `pi//8` b. `pi//6` c. `pi//4` d. `pi//36`

A

`pi//8`

B

`pi//6`

C

`pi//4`

D

`pi//36`

Text Solution

Verified by Experts

The correct Answer is:
A
We have
`pi/4=(1-1/3)+(1/5-1/7)+(1/9-1/11)+…`
`=2/(1xx3)+2/(5xx7)+2/(9xx11)+..`
`rArr1/(1xx3)+1/(5xx7)+1/(9xx11)+..=pi/8`
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CENGAGE-PROGRESSION AND SERIES-Exercise (Single)
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  8. If Hn=1+12++1/ndot , then the value of Sn=1+3/2+5/3++(99)/(50) is H(50...

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  9. The sum to 50 terms of the series 3/1^2+5/(1^2+2^2)+7/(1^+2^2+3^2)+...

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  10. Let S=4/19+44/(19)^2+444/(19)^3+...oo then find the value of S

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  11. If 1-1/3+1/5-1/7+1/9-1/(11)+=pi/4 , then value of 1/(1xx3)+1/(5xx7)+1/...

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  12. If 1/(1^2)+1/(2^2)+1/(3^2)+ tooo=(pi^2)/6,t h e n1/(1^2)+1/(3^2)+1/(5^...

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  13. lim(nrarroo) Sigma(r=1)^(n) (r)/(1xx3xx5xx7xx9xx...xx(2r+1)) is equal ...

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  14. The greatest interger by which 1+Sigma(r=1)^(30) rxxr ! is divisible...

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  15. If Sigma(r=1)^(n) r^4=I(n), " then "Sigma(r=1)^(n) (2r -1)^4 is equal ...

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  17. If x1,x2 …,x(20) are in H.P and x1,2,x(20) are in G.P then Sigma(r=1)^...

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  18. Find the value of Sigma(r=1)^(n) (a+r+ar)(-a)^r is equal to

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