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If agt0, then sum(n=1)^(oo) ((a)/(a+1))^...

If `agt0`, then `sum_(n=1)^(oo) ((a)/(a+1))^(n)` equals

A

`(a+1)/(2a+1)`

B

`(a)/(2a+1)`

C

a+1

D

a

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`underset(n=1)overset(oo)sum((a)/(a+1))^(n)=a["Using "a+ar+ar^(2)+ . . . oo=(a)/(1-r)]`
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OBJECTIVE RD SHARMA-SEQUENCES AND SERIES-Chapter Test
  1. If agt0, then sum(n=1)^(oo) ((a)/(a+1))^(n) equals

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  2. Let H(n)=1+(1)/(2)+(1)/(3)+ . . . . .+(1)/(n), then the sum to n terms...

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  3. The sum to n terms of the series 1/2+3/4+7/8+15/16+..... is given by

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  4. If A(1),A(2) are between two numbers, then (A(1)+A(2))/(H(1)+H(2)) is ...

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  5. if (m+1)th, (n+1)th and (r+1)th term of an AP are in GP.and m, n and r...

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  6. Given that n arithmetic means are inserted between two sets of numbers...

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  7. If a,b, and c are in G.P then a+b,2b and b+ c are in

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  8. If in a progression a1, a2, a3, e t cdot,(ar-a(r+1)) bears a constant...

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  9. If in an AP, t1 = log10 a, t(n+1) = log10 b and t(2n+1) = log10 c then...

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  10. Find the sum of the series: 1^2-2^2+3^2-4^2+.....-2008^2+2009^2.

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  11. If4a^(2)+9b^(2)+16c^(2)=2(3ab+6bc+4ca)," where "a,b,c are non-zero num...

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  12. If Sn denotes the sum of n terms of an A.P. whose common difference is...

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  13. The sides of a right angled triangle arein A.P., then they are in the...

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  14. Find the sum of all the 11 terms of an AP whose middle most term is 30...

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  15. The maximum sum of the series 20+19 1/3+18 2/3+ is 310 b. 300 c. 0320 ...

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  16. If three numbers are in G.P., then the numbers obtained by adding the ...

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  17. If p,q,r,s in N and the are four consecutive terms of an A.P., then p^...

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  18. If x,y,z be three positive prime numbers. The progression in which sqr...

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  19. If 1/(b-a)+1/(b-c)=1/a+1/c , then a ,b ,a n dc are in H.P. a ,b ,a n d...

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  20. If three numbers are in H.P., then the numbers obtained by subtracting...

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  21. The first three of four given numbers are in G.P. and their last three...

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