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

If `|a| lt 1 ` and |b|` lt` 1 , then the sum of the series
`a(a+b) + a^2 (a^2 + b^2) + a^3 (a^3 + b^3) `+… upto `oo` is :

A

`a^2/b+1`

B

`a^2/(1-ab)`

C

`a^2/(1-a^2)+(ab)/(1-ab)`

D

`a^2/b^2+1/(ab)`

Text Solution

Verified by Experts

The correct Answer is:
C
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QUANTUM CAT-SEQUENCE, SERIES & PROGRESSIONS-QUESTION BANK
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  2. The sum of n terms of the series 1^2 + (1^2 + 3^2) + (1^2 + 3^2 + 5...

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  3. If |a| lt 1 and |b| lt 1 , then the sum of the series a(a+b) + a^2...

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  4. Find the sum to n terms of the series 3//(1^2xx2^2)+5//(2^2xx3^2)+7//(...

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  5. The natural numbers are written as follows : The sum of numbers...

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  6. The number ubrace(1111.....1)("119 times") is a:

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  7. The interior angles of a polygon are in A.P. If the smallest angle is ...

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  8. log(10)10+log(10)10^(2)+ . . .+log(10)10^(n)

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  9. The value of 0.1bar23 is:

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  10. If n is a positive integer, then ubrace(111...1)("2n times")-ubrace(22...

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  11. One side of an equilateral triangle is 24 cm. The midpoints of its sid...

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  12. The odd positive intergers are arranged in a triangle as follows: ...

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  13. Find the sum to n terms of the series log a+ log"" (a^3)/(b) + log ...

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  14. The value of 0. 2^(logsqrt(5)1/4+1/8+1/(16)+) is 4 b. log4 c. log2 d....

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  15. If a, b, c are in H.P. , then (b+a)/(b-a)+(b+c)/(b-c)

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  16. Let a,b,c are in G.P. with common ratio r(0ltrlt1). Then a,2b,3c are i...

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  17. Find the sum of the series (5)/(13)+(55)/(13)^2+(555)/(13)^2+(5555)/((...

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  18. Sum of infinite series 1/(1*4)+1/(4*7)+1/(7*10)+......oo is

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  19. A sequence a1,a2,a3,.an of real numbers is such that a1=0, |a2|=|a1+1|...

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  20. Find the sum of the squares of first 50 natural numbers

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