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If sum of the series `(1)/(x+1)+(1)/(x(x+2))+(1)/(x(x+1)(x+3))+...+(1)/(x(x+1)...(x+99)(x+100))+(1)/(x(x+1)(x+2)...(x+100)(x+101))` is `(2)/(3)`, then x is equal to

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MCGROW HILL PUBLICATION-PROGRESSIONS-EXERCISES (Numerical Answer Type Questions)
  1. Let S= overset(oo)underset(r=1)Sigma (r )/(r^(4)+4), then 2S=

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  2. Let A(1), A(2),.., A(75) be 75 arithmetic means inserted between two d...

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  3. Suppose (1)/(a(1)),(1)/(a(2)),….,(1)/(a(201)) is in A.P., then overset...

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  4. Let S=(0.7)^(log(0.49)((1)/(8)+(1)/(8^(2))+(1)/(8^(3))+...),

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  5. Suppose a, b gt 0. Let a,A(1),A(2),…,A(25), b be in A.P., a G(1),G(2),...

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  6. Suppose overset(oo)underset(r=1)Sigma t(r) =3^(n)-1 AA n in N" then "o...

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  7. If the sum to n terms of the series (3)/((1^(2))(2^(2)))+(5)/((2^(2))(...

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  8. Let S = Sum of the series (1)/(4^(2)+2)+(1)/(5^(2)+3)+(1)/(6^(2)+4)+(1...

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  9. Let S=(1)/(1xx3xx5)+(1)/(3xx5xx7)+(1)/(5xx7xx9)+(1)/(7xx9xx11)+…" upto...

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  10. Let a = coefficient of x^(20) in (1+x+2x^(2)+3x^(3)+…+20x^(20))^(2)," ...

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  11. Let overset(n)underset(r=1)Sigma overset(r )underset(j=1)Sigma overset...

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  12. Sum of the series 2.5+(1)/(2)+(1)/(3)+(1)/(2^(2))+(1)/(3^(2))+(1)/(3^(...

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  13. Suppose a,b,c gt 0. If (2)/(a+b),(1)/(b),(2)/(b+c) are in A.P., then (...

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  14. Suppose a,b,c gt 1 and n in N, n ge 2. If log(a)(n),log(b)(n),log(c )(...

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  15. Given sum of first n terms of an A.P. is 2n + 3n^(2). rel then Another...

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  16. Suppose a,b,c ne R and satisfy (i) 2 lt a, b, c lt 18 (ii) a+b+c=25 ...

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  17. If sum of the series (1)/(x+1)+(1)/(x(x+2))+(1)/(x(x+1)(x+3))+...+(1)/...

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  18. If sum of the series overset(oo)underset(j=0)Sigma overset(oo)underset...

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  19. Suppose k ne N is fixed then sum of the series (1)/(k^(2))overset(oo)u...

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