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Let S=4/19+44/(19)^2+444/(19)^3+...oo th...

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

A

`40//9`

B

`38//81`

C

`36//171`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`S=4/19+44/19^(2)+444/19^(3)+…` (1)
`rArr1/19S=4/19^(2)+44/19^(3)+…` (2)
Subtracting (2) from (1), we get
`18/19S=4/19+40/19^(2)+400/19^(3)+…`
`=(4/19)/(1-10/19)=4/9`
`rArrS=38/81`
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CENGAGE-PROGRESSION AND SERIES-Exercise (Single)
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  5. The sum of series Sigma(r=0)^(r) (-1)^r(n+2r)^2 (where n is even) is

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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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  16. Value of (1+1/3)(1+1/(3^2))(1+1/(3^4))(1+1/(3^8))oo is equal to 3 b. 6...

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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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  19. The sum of series x/(1-x^2)+(x^2)/(1-x^4)+(x^4)/(1-x^8)+ to infinite t...

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  20. The sum of 20 terms of the series whose rth term s given by kT(n)=(-1)...

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