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If the sum of the series 1+ (3)/(x) + (9...

If the sum of the series `1+ (3)/(x) + (9)/(x^(2))+ (27)/(x^(3)) + …oo` is a finite number, then

A

`x lt 3`

B

`x gt 1//3`

C

`x lt 1//3`

D

`x gt 3`

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The correct Answer is:
D
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AAKASH SERIES-SEQUENCE AND SERIES-Practice Exercise
  1. Let a(1), a(2) ….a(10) be A.P and h(1), h(2)…h(10) be in H.P. If a(1)=...

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  2. If p th term of a H.P is qr and q^(th) term is r p then r^(th) term is

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  3. If the sum of the series 1+ (3)/(x) + (9)/(x^(2))+ (27)/(x^(3)) + …oo ...

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  4. If 3 + (3 + d) (1)/(4) + (3+ 2d) (1)/(4^(2)) + …oo= 8 then d=

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  5. If 1+ 2x + 3x^(2) + 4x^(3) + …oo= (9)/(4) (|x| lt 1) then x=

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  6. If the sum to infinity of the series 3 + 5x + 7x^(2) + …oo = (44)/(9) ...

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  7. Let p= 3^(1//3) .3^(2//9).3^(3//27) ….oo then p^(1//3)=

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  8. If (a + b e^(x))/(a-b e^(x)) = (b + c e^(x))/(b- c e^(x))= (c + d e^(x...

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  9. Given sum of the first n terms of an A.P is 2n+ 3n^(2). Another A.P is...

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  10. The sum (3)/(1^(2)) + (5)/(1^(2) + 2^(2)) + (7)/(1^(2)+ 2^(2) + 3^(2))...

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  11. Given a sequence of 4 numbers, first three of which are in G.P.,and th...

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  12. The value of 1^(2) + 3^(2) + 5^(2) + …+ 25^(2) is

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  13. Let a(1), a(2), a(3)….. be terms of an A.P. If (a(1) + a(2) + …..a(p))...

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  14. The sum of the series 2^(2) + 2(4^(2)) + 3(6^(2)) + ….upto 10 terms is

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  15. If S= tan^(-1) ((1)/(n^(2) +n+1)) + tan^(-1) ((1)/(n^(2) + 2n+ 3))+ …....

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  16. If a(1), a(2), a(3),…, a(n) are in A.P such that a(4) - a(7) + a(10)= ...

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  17. Given an A.P whose terms are all positive integers. The sum of its nin...

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  18. If the sum (3)/(1^(2)) + (5)/(1^(2) + 2^(2)) + (7)/(1^(2) + 2^(2) + 3^...

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  19. In a geometric progression, if the ratio of the sum of first 5 terms t...

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  20. The sum of the first 20 terms common between the series 3+7 + 11 + 15…...

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