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The value of C(0)+3C(1)+5C(2)+7C(3)+ ....

The value of
`C_(0)+3C_(1)+5C_(2)+7C_(3)+ . . .+(2n+1)C_(n)` is:

A

`2^(n) `

B

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

C

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

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
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HIMALAYA PUBLICATION-BINOMIAL THEOREM-QUESTION BANK
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  2. Let (1+x^(2))^(2)(1+x)^(n) = sum(k=0)^(n+4) a(k) x^(k) . If a(1) , a...

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  3. The value of C(0)+3C(1)+5C(2)+7C(3)+ . . .+(2n+1)C(n) is:

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  4. The largest term in the expansion of (3+2x)^(50) where x=1/5 is:

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  6. The positive integer just greater than, (1+0.0001)^(10000) is

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  7. In the binomial expansion of (a-b)^(n),nge5, the sum of the 5th and 6t...

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  8. The sum of series: ""^(20)C(0)-""^(20)C(1)+""^(20)C(2)-""^(20)C(3)+ ...

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  9. If the coefficient of x^(7) in the expansion of (ax^(2)+b^(-1)x^(-1))^...

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  10. The remainder left out when 8^(2n)-(62)^(2n+1) is divided by 9 is

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  11. The coefficient of x^(7) in the expansion of (1-x-x^(2)+x^(3))^(6) is:

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  13. In the expansion of (x+sqrt(x^(2)-1))^(6)+(x-sqrt(x^(2)-1))^(6) the...

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  14. The coefficient of x^(6) in the expansion of (1+x+x^(2))^(-3) is

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  15. The coefficient of x^(4) in the expansion of ((x)/(2)-(3)/(x^(2)))^(...

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  16. The coefficient of the middle term in the expansion of (1+x)^(2 n) is

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  17. The greatest coefficient in the expansion of (1+x)^(10) is

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  18. If the second term in the expansion ((a)^(1/13)+(a)/(sqrt(a^(-1))))^...

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  19. The coefficient of x^(20) in (1+3 x+3 x^(2)+x^(3))^(20) is

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  20. The greatest term in the expansion of (1+3 x)^(54) , when x=(1)/(3) ...

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