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Let S=overset(oo)underset(n=1)Sigma(5^(n...

Let `S=overset(oo)underset(n=1)Sigma(5^(n)7^(n))/((7^(n)-5^(n))(7^(n+1)-5^(n+1)))` then S=

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MCGROW HILL PUBLICATION-PROGRESSIONS-SOLVED EXAMPLES LEVEL (Numerical Answer Type Questions)
  1. The number of terms common between the series 1+ 2 + 4 + 8..... to 100...

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  2. If x gt 0 and log(3) (x)+log(3)(x^(1//3))+log(3)(x^(1//9))+log(3)(x^(1...

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  3. If a1,a2,a3,a4 are in HP , then 1/(a1a4)sum(r=1)^3ar a(r+1) is roo...

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  4. Let s(n)=1+(1)/(3)+(1)/(3^(2))+…+(1)/(3^(n-1)). The least value of n i...

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  5. Let a(n) be the nth term of a G.P. of positive real numbers. If overse...

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  6. Let [x] = greatest integer le x. Suppose roots of the quadratic equati...

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  7. three number a,b,c are in GP such that : (i) a+b+c=70 (ii) 4a,5b,4c a...

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  8. Suppose a(1),a(2),…a(n) are positive real numbers which are in A.P. If...

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  9. Suppose alpha, gamma are roots of the equation ax^(2)-4x+1=0 and beta,...

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  10. Let an is a positive term of a GP and sum(n=1)^100 a(2n + 1)= 200, sum...

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  11. Suppose a(1),a(2),… are real numbers such that sqrt(a(1))+sqrt(a(2)-1)...

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  12. Let S=overset(oo)underset(n=1)Sigma(5^(n)7^(n))/((7^(n)-5^(n))(7^(n+1)...

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  13. Let S=overset(oo)underset(k=1)Sigma (k(10)^(k)+2^(k+1)5^(k))/(5^(k)2^(...

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  14. Consider an A.P. a1, a2, an , and the G.P. b1,b2, ,bn , such that a...

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  15. Suppose a(1),a(2),…a(201) gt 0 and are in G.P. If a(101)=36 and overse...

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  16. Let P(n) denote the product of first n terms of the G.P. 16, 4, 1, 1/4...

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  17. Suppose x, y in N and log(5)(x)+log(5)(x^(1//2))+log(5)(x^(1//4))+….=y...

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  18. The coefficient of the quadratic equation a x^2+(a+d)x+(a+2d)=0 are co...

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  19. Suppose 1 lt a lt sqrt(e) and log(e)a^(2)+(log(e)a^(2))^(2)+(log(e)a^(...

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  20. For k=2,3,…, let S(k) denote the sum of the infinite G.P. whose first ...

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