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Find the sum of the series 1+(4)/(5)+(7)...

Find the sum of the series `1+(4)/(5)+(7)/(5^(2))+(10)/(5^(3))+"....."`
(ii) to infinity.

A

`(16)/(35)`

B

`(11)/(8)`

C

`(35)/(16)`

D

`(8)/(6)`

Text Solution

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The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-SEQUENCES AND SERIES-Exercise
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  6. Find the sum 1+(1+2)+(1+2+2^(2))+(1+2+2^(2)+2^(3))+ …. To n terms.

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  7. If a,b,c are in H.P., then the value of ((1)/(b)+(1)/(c)-(1)/(a))((1...

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  8. The 5th term of the series (10)/(9),(1)/(3)sqrt((20)/(3)),(2)/(3),… is

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  10. If d,e,f are G.P. and the two quadratic equations ax^(2)+2bx+c=0andd...

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  11. The sum of n terms of the following series 1+(1+x)+(1+x+x^2)+.... will...

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  12. For a sequence {a(n)}, a(1) = 2 and (a(n+1))/(a(n)) = 1/3, Then unders...

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  13. In an arithmetic sequence a(1),a(2),a(3), . . . . .,a(n), Delta=|{:(...

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  17. If H1. H2...., Hn are n harmonic means between a and b(!=a), then the ...

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  18. If a,b,c be respectively the p^(th),q^(th)andr^(th) terms of a H.P., ...

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  19. If a ,b ,c are in G.P. and a-b ,c-a ,a n db-c are in H.P., then prove ...

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