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The sum of the series 2/3+8/9+(26)/(27)+...

The sum of the series `2/3+8/9+(26)/(27)+(80)/(81)+` to `n` terms is `(a) n-1/2(3^(-n)-1)` (b) `n-1/2(1-3^(-n))` (c) `n+1/2(3^n-1)` (d) `n-1/2(3^n-1)`

A

`n-(1)/(2)(3^(-n)-1)`

B

`n-(1)/(2)(1-3^(-n))`

C

`n+(1)/(2)(3^(n)-1)`

D

`n-(1)/(2)(3^(n)-1)`

Text Solution

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The correct Answer is:
A
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OBJECTIVE RD SHARMA ENGLISH-SEQUENCES AND SERIES-Chapter Test
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  4. If a\ (1/b+1/c),\ b(1/c+1/a),\ c(1/a+1/b) are in A.P. prove that a ,\ ...

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  5. If the m^(th),n^(th)andp^(th) terms of an A.P. and G.P. be equal and b...

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  6. The 7th term of a H.P. is (1)/(10) and 12 th term is (1)/(25), find th...

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  7. The length of side of a square is 'a' metre. A second square is formed...

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  8. The harmonic mean of the roots of the equation (5+sqrt(2))x^2-(4+sqrt(...

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  9. If three positive real numbers a,b,c, (cgta) are in H.P., then log(a+c...

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  10. In an A.P., the p^(th) term is 1/q and the q^(th) term is 1/p. fin...

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  11. The sum of the series 2/3+8/9+(26)/(27)+(80)/(81)+ to n terms is (a) n...

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  12. If a,b,c are in H.P. , then

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  13. The odd value of n for which 704+1/2(704)+… upto n terms = 1984-1/2(1...

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  14. The positive interger n for which 2xx2^2+3xx 2^3+4xx2^4+….+nxx2^4=2^(n...

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  15. If 1^2+2^2+3^2++2003^2=(2003)(4007)(334) and (1)(2003)+(2)(2002)+(3)(2...

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  16. The sum to n terms of the series (n^(2)-1^(2))+2(n^(2)-2^(2))+3(n^(2...

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  17. The sum of the series a-(a+d)+(a+2d)-(a+3d)+... up to (2n+1) terms is:...

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  18. If Hn=1+1/2+...+1/ndot , then the value of Sn=1+3/2+5/3+...+(99)/(50) ...

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  19. Sum of the first n terms of the series 1/2+3/4+7/8+(15)/(16)+............

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  20. If a(n)=1+(1)/(2)+(1)/(3)+(1)/(4)+(1)/(5)+ . . . .+(1)/(2^(n)-1), then

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