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Find the sum 1+(1+2)+(1+2+2^(2))+(1+2+2^...

Find the sum `1+(1+2)+(1+2+2^(2))+(1+2+2^(2)+2^(3))+` …. To n terms.

A

`2^(n+2)-n-4`

B

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

C

`2^(n+1)-n`

D

`2^(n+1)-1`

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The correct Answer is:
A
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OBJECTIVE RD SHARMA ENGLISH-SEQUENCES AND SERIES-Exercise
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  2. the determinant |{:(a,,b,,aalpha+b),(b,,c,,balpha+c),(aalpha+b,,balpha...

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  3. Find the sum 1+(1+2)+(1+2+2^(2))+(1+2+2^(2)+2^(3))+ …. To n terms.

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

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

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  6. If x^(18)=y^(21)=z^(28), then 3,3 log(y)x,3log(z)y,7log(x)z are in

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

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

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

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

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  11. Prove that {:((666 ….6)^2+(888….8)=4444…..4),(" ""n digits " " ...

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  12. Thr ciefficient of x^(n-2) in the polynomial (x-1)(x-2)(x-3)"…."(x-n),...

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  13. The sum of the series 1^(2)+1+2^(2)+2+3^(2)+3+ . . . . .. +n^(2)+n, is

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

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

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  16. 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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  17. The cubes of the natural numbers are grouped as 1^(3),(2^(3),3^(3)),(4...

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  18. If a\ a n d\ b are the roots of x^2-3x+p=0\ a n d\ c ,\ d are the root...

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  19. Let the sum of n, 2n, 3n terms of an A.P. be S1,S2and S3, respectively...

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  20. If a ,b ,c ,d ,e ,f are A.M.s between 2 and 12, then find the sum a+b+...

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