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If x = sum(n = 0)^(infty) a^(n) , y = su...

If `x = sum_(n = 0)^(infty) a^(n) , y = sum_(n = 0)^(infty) b^(n) , z = sum_(n=0)^(infty) c^(n)` where a,b,c are in A.P . And `|a| lt 1, |b| lt 1, |c| lt ,` then x,y,z, are in

A

G.P

B

A.P.

C

Arithmetic - Geometric Progression

D

H.P.

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The correct Answer is:
D
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DIPTI PUBLICATION ( AP EAMET)-SEQUENCES AND SERIES -EXERCISE
  1. If |x| lt 1, y = x - x^(2) + x^(3) - x^(4) + ….. , the value of x in t...

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  2. If x = 1 + a + a^(2) + …. infty " , " y = 1 + b + b^(2) + …...

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  3. If x = sum(n = 0)^(infty) a^(n) , y = sum(n = 0)^(infty) b^(n) , z = s...

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  4. If exp{ (sin^(2) x + sin^(4) x + sin^(6) x + …. "Upto" infty) log(e) 2...

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  5. If exp { (tan^(2) x -tan^(4) x + tan^(8) x - tan^(6) x …. ) log(e) 16 ...

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  6. For 0 lt x lt pi the values of x which satisfy the relation 9^(1 + ...

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  7. Given that 0 lt x lt (pi)/(4), (pi)/(4) lt y lt (pi)/(2) and sum(k = 0...

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  8. The coefficient of x in (x^2 +(c )/(x))^5 is

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  9. (1)/(2) + (1)/(4) + (1)/(8) + (1)/(16) + ….. = x , (1)/(3) + (1)/(9) +...

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  10. the sum to infinity of (1)/(7) + (2)/(7^(2)) + (1)/(7^(3)) + (2)/(7^(4...

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  11. The sum of an infinite G.P. is 2. If the sum of their squares is 4/3, ...

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  12. The least value of n for which 1 + 2 + 2^(2) + …… to n terms is great...

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  13. If x gt 0, and log(2) + log(2)(sqrt(x)) + log(2) (4sqrt(x)) + log(2) (...

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  14. If (1 + 3 + 5 + …. +P ) + (1 + 3 + 5 + …. Q) = (1 + 3 + 5 + … r) where...

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  15. The greatest value on n so that 1 + 5 +5^(2) + 5^(3) + …. N terms is ...

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  16. 7 + 77 + 777 + …. N terms =

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  17. 6 + 66 + 666 + ….n terms =

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  18. The sum to n terms of the series .5 + .55 + .555 + ….. Is

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  19. 7 + 77 + 777 + …. N terms =

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  20. The sum of first 20 terms of the sequence 0.7, 0.77, 0.777,….. Is

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