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Let Sk be sum of an indinite G.P whose f...

Let `S_k` be sum of an indinite G.P whose first term is 'K' and commmon ratio is `(1)/(k+1)`. Then `Sigma_(k=1)^(10) S_k` is equal to _________.

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The correct Answer is:
65
`S_(k)=k/(1-1/(k+1))=k+1`
`aum_(k=1)^(10)S_(k)=sum_(k=1)^(10)(k+1)=(10xx11)/2+10=65`
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CENGAGE-PROGRESSION AND SERIES-Exercise (Numerical)
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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/(20...

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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 value 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) (r^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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