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If nth term of series is 2^(n) + n, then...

If nth term of series is `2^(n)` + n, then sum of n terms =

A

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

B

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

C

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

D

none

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The correct Answer is:
C
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DIPTI PUBLICATION ( AP EAMET)-SEQUENCES AND SERIES -EXERCISE
  1. Which term of the series 1,2,4,8,……… is 256?

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  2. Sum of 20 terms of 3 + 6 + 12 + …. Is

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  3. If nth term of series is 2^(n) + n, then sum of n terms =

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  4. If 5th term of a G.P is 32 and common ratio 2, then the sum of 14 term...

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  5. How many terms of the series 1 + 3 + 9 + …. Sum to 364 ?

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  6. If (1 - y) (1 + 2x + 4x^(2) + 8x^(3) + 16x^(4) + 32x^(5)) = 1 -y^(6), ...

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  7. In a geometric progression consisting of positive terms each term equa...

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  8. 1 + (0.04) + (0.04)^(2) + …. infty =

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  9. If |x| lt 1, y = x - x^(2) + x^(3) - x^(4) + ….. , the value of x in t...

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

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

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

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

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

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

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

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  17. (1)/(2) + (1)/(4) + (1)/(8) + (1)/(16) + ….. = x , (1)/(3) + (1)/(9) +...

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

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

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

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