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The sum of first n terms of the series 1...

The sum of first `n` terms of the series `1 + (1 + x) y+ (1 + x + x^(2)) y^(2) + (1 + x + x^(2) + x^(3))y^(3) + ………..` is

A

`(1/(1 - x))[(1-y^(n))/(1 - y) - y ((1 - x^(n)y^(n))/(1 - xy))]`

B

`(1/(1 - x))[(1-y^(n))/(1 - y^(2)) - x ((1 - x^(n)y^(n))/(1 - xy))]`

C

`(1/(1 - x))[(1-y^(n))/(1 - y) - x^(2) ((1 - x^(n)y^(n))/(1 - xy))]`

D

`(1/(1 - x))[(1-y^(n))/(1 - y) - 2x ((1 - x^(n)y^(n))/(1 - xy))]`

Text Solution

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The correct Answer is:
D
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NEW JOYTHI PUBLICATION-SEQUENCES AND SERIES -QUESTIONS FROM COMPETITIVE EXAMS
  1. In an A.P., the first term is 2 and the sum of first five terms is 5. ...

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  2. If a, b, c, d are in G.P., then (a + b + c + d)^(2) is equal to

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  3. The sum of first n terms of the series 1 + (1 + x) y+ (1 + x + x^(2)) ...

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  4. If 3^(rd), 7^(th) and 12^(th) terms of A.P. are three consecutive term...

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  5. If a(1) = 4 and a(n + 1) = a(n) + 4n for n gt= 1, then the value of a(...

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  6. If the first term of a G.P. is 729 and its 7^(th) term is 64, then the...

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  7. Let a(1), a(2), a(3), a(4) be in A.P. If a(1) + a(4) = 10 and a(2)a(3)...

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  8. The 100^(th) term of the sequence 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, ……. is

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  9. Let S(n) denote the sum of first n terms of an A.P. If S(4) = -34,S(3)...

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  10. An A.P. has the property that the sum of first ten terms is half the s...

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  11. The sum of the series sum(n =8)^(17)1/((n + 2)(n + 3)) is equal to

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  12. If two positive numbers are in the ratio 3 + 2sqrt(2) : 3 - 2sqrt(2), ...

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  13. Let x(1), x(2), …… , x(n) be in an A.P. If x(1) + x(4) + x(9) + x(11) ...

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  14. If the second and fifth terms of a G.P. are 24 and 3 respectively, the...

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  15. If the sum of first 75 terms of an A.P. is 2625, then the 38^(th) term...

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  16. If -5, k, -1 are in A.P., then the value of k is equal to

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  17. Let T(n) denote the number of triangles which can be formed by using t...

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  18. if 1,log(9)(3^(1 - x) + 2),log(3)[4.3^(x) - 1] are in A.P. then x equa...

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  19. 1^(3) - 2^(3) + 3^(3) + 4^(3) + .... + 9^(3) =

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  20. Sum of infinite number of terms in GP is 20 and sum of their square is...

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