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If |a| lt 1 and |b| lt 1, then the sum o...

If `|a| lt 1 and |b| lt 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-ab))`

C

`(1)/((1-b ) (1-ab))`

D

`(1)/((1-a) (1-b) (1-ab))`

Text Solution

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The correct Answer is:
C
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AAKASH SERIES-SEQUENCE AND SERIES-Practice Exercise
  1. If |a| lt 1 and |b| lt 1, then the sum of the series 1 + (1+a) b + (1 ...

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  2. If sum of the series a- (a+d) + (a+ 2d)- (a + 3d) +….up to 21 terms is

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  3. The first term of an A.P of consecutive integers is p^(2) + 1 . The su...

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  4. The sum of n terms of an A.P is 3n^(2) +n. Then 8^(th) term of the A.P...

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  5. The ratio between the sum of n terms of two A.P.'s is 3n+8: 7n+15. The...

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  6. The sum of all integers between 50 and 500 which are divisible by 7 is

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  7. If 5^(th) term of A.P is (1)/(6) and 6^(th) term of A.P is (1)/(5) the...

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  8. The interior angles of a polygon are in A.P. if the smallest angle is ...

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  9. The sum of r terms of an A.P. is denoted by S(r ) and (S(m+1))/(S(n+1)...

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  10. The n^(th) term of an A.P is p and the sum of the first n terms is s. ...

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  11. If s(1), s(2), s(3)…..s(p) are the sums of n terms of 'p' A.P's whose ...

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  12. If a(1), a(2), a(3)…..a(n) are in A.P. with common difference d then s...

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  13. If S(1), S(2), S(3) be the sum of 10, 20, 30 terms respectively of an ...

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  14. The first, second and last terms of an A.P. are a, b, c respectively, ...

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  15. If the sum of the first ten terms of an A.P is four times the sum of i...

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  16. If a,b,c are in A.P then a((1)/(b) + (1)/(c )), b ((1)/(c ) + (1)/(a))...

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  17. If p, q, r are in A.P the p^(2) (q + r), q^(2) (r + p), r^(2) (p+q) ar...

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  18. If the A.M. between p^(th) and q^(th) terms of an A.P be equal to A.M ...

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  19. If n A.M's are inserted between two quantites a and b then their sum i...

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  20. If n A.M.'s are inserted between 4 and 96 then sum of n A.M.'s is

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  21. If n A.M.'s are inserted between 20 and 80 such that the ratio of firs...

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