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If |a|<1a n d|b|<1, then the sum of the ...

If `|a|<1a n d|b|<1,` then the sum of the series `1+(1+a)b+(1+a+a^2)b^2+(1+a+a^2+a^3)b^3+...` is (a) `1/((1-a)(1-b))` (b). `1/((1-a)(1-a b))` (c.) `1/((1-b)(1-a b))` (d.) `1/((1-a)(1-b)(1-a b))`

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  1. Consider an A.P. a1, a2, a3,......... such that a3+a5+a8=11 and a4+a2...

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  2. If the sum of n terms of an A.P is cn (n-1) where c ne 0 then find the...

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  3. If |a|<1a n d|b|<1, then the sum of the series 1+(1+a)b+(1+a+a^2)b^2+(...

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  4. Find the sum of odd intergers from 1 to 201.

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  5. If a1, a2, a3(a1>0) are three successive terms of a G.P. with common r...

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  6. Three numbers form an increasing G.P. If the middle number is doubled,...

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  7. If S1,S2, S3, Sm are the sums of n terms of m A.P. ' s whose first ter...

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  8. If S1,S2 and S3 be respectively the sum of n, 2n and 3n terms of a G.P...

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  9. There are 4n + 1 terms in a sequence of which first 2n + 1 are in Arit...

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  10. If (p+q)t h term of a G.P. is a and its (p-q)t h term is b where a ,b ...

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  11. Find the sum of n terms of the series whose nth term is T(n)=tanx/(2^n...

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  12. Evaluate, sum(i = 0)^iinfty sum(j = 0)^infty sum(k = 0)^infty 1/(3^i c...

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  13. The first trem of a GP is -3 and the square of the second term is equa...

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  14. If log(2)(5.2^(x)+1),log(4)(2^(1-x)+1) and 1 are in A.P,then x equals

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  15. Find the geometric series whose 5th and 8th terms are 80 and 640 respe...

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  16. 0ltthetaltpi/2, if x=sum(n=0)^inftycos^(2n)theta,y=sum(n=0)^inftysin^(...

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  17. The real numbers x1, x2, x3 satisfying the equation x^3-x^2+b x+gamma=...

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  18. Let a, b, c, d be real numbers in G.P. If u, v, w satisfy the system...

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  19. The 5th, 8th and 11th terms of a GP are a,b,c respectively. Show that...

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  20. If (log)3 2,(log)3(2^x-5)a n d(log)3(2^x-7/2) are in arithmetic progre...

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