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If Sigma(r=1)^(50) (2)/(r^2+(11-r^2)), t...

If `Sigma_(r=1)^(50) (2)/(r^2+(11-r^2))`, then the value of n is __________

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Verified by Experts

The correct Answer is:
50
`S=1/(2^(0)+2^(50))+1/(2^(1)+2^(50))+..+1/(2^(100)+2^(50))`
`S=1/(2^(100)+2^(50))+1/(2^(99)+2^(50))+…+1/(2^(0)+2^(50))`
`2S=1/(2^(50)+1/(2^(50))+..` 100 times
`thereforeS=50/(2^(50))`
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Sigma_(r=1)^(50)(r^2)/(r^2+(11-r)^2) is equal to ______.

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CENGAGE-PROGRESSION AND SERIES-Exercise (Numerical)
  1. The terms a1, a2, a3 from an arithmetic sequence whose sum s 18. The t...

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  2. Let the sum of first three terms of G.P. with real terms be 13/12 and ...

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  3. The first term of an arithmetic progression is 1 and the sum of the fi...

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  4. A person drops a ball from an 80 m tall building and each time the bal...

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  5. The digits in units's place of number (10^(2013)-1)/(10^33-1) is..

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  6. The number of positive integral ordered pairs of (a ,b) such that 6,a ...

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  7. If the roots of 10 x^3-n x^2-54 x-27=0 are in harmonic oprogresi...

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  8. Given a,b,c are in A.P.,b,c,d are in G.P and c,d,e are in H.P .If a=2 ...

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  9. Let Sk be sum of an indinite G.P whose first term is 'K' and commmon r...

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  10. The value of the sum Sigma(i=1)^(20) i(1/i+1/(i+1)+1/(i+2)+.....+1/(2)...

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  11. The difference between the sum of the first k terms of the series 1^3+...

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  12. The vlaue of the Sigma(n=0)^(oo) (2n+3)/(3^n) is equal to .

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  13. The sum of the infinite Arithmetico -Geometric progression3,4,4,… is .

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  14. Sigma(r=1)^(50)(r^2)/(r^2+(11-r)^2) is equal to .

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  15. If Sigma(r=1)^(50) (2)/(r^2+(11-r^2)), then the value of n is

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  16. Let lt an gt be an arithmetic sequence of 99 terms such that sum of it...

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  17. Find the sum of series upto n terms ((2n+1)/(2n-1))+3((2n+1)/(2n-1))^2...

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  18. Let S=Sigma(n=1)^(999) (1)/((sqrt(n)+sqrt(n+1))(4sqrt(n)+4sqrtn+1)) , ...

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  19. Let S denote sum of the series 3/(2^3)+4/(2^4 .3)+5/(2^6 .3)+6/(2^7 .5...

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  20. The sum (7)/(2^2xx5^2)+13/(5^2xx8^2)+19/(8^2xx11^2)+…10 terms is S, th...

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