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Find the following sum : (1)/(n!) + (1...

Find the following sum :
`(1)/(n!) + (1)/(2!(n-2)!) + (1)/(4!(n-4)!)+"...."`.

A

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

B

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

C

`(2^(n))/(n!)`

D

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

Text Solution

Verified by Experts

The correct Answer is:
B
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OBJECTIVE RD SHARMA ENGLISH-BINOMIAL THEOREM AND ITS APPLCIATIONS -Chapter Test
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  2. The value of C(0)+3C(1)+5C(2)+7C(3)+….+(2n+1)C(n) is equal to :

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  3. Find the following sum : (1)/(n!) + (1)/(2!(n-2)!) + (1)/(4!(n-4)!)+...

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  4. The coefficient of x^(n) y^(n) in the expansion of [(1 + x)(1+y) (x...

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  5. If (1 + x - 2 x^(2))^(6) = 1 + C(1) x + C(2) x^(2) + C(3) x^(3) + …+ C...

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  6. Find the ratio of the coefficient of x^(15) to the term independent of...

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  7. Find the number of terms in the expansion of (x+y+z)^(n).

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  8. In the expansion of (1+x)^30 the sum of the coefficients of odd powers...

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  9. In the expansion of (x^(2) + 1 + (1)/(x^(2)))^(n), n in N,

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  10. The term independent ofx in the expansion of (1+x)^10*(1+1/x)^10 is

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  11. In the expansion of (x^(3) - (1)/(x^(2)))^(15) , the constant term,i...

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  12. The middle term in the expansion of (1 - (1)/(x))^(n) (1 - x)^(n) is

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  13. The total number of terms which are dependent on the value of x in the...

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  14. The coefficient of x^6 in {(1+x)^6+(1+x)^7+........+(1+x)^(15)} is

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  15. The number of real negative terms in the binomial expansion of (1+i x)...

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  16. Find the number of terms in the expansion of (x+sqrt(x^2-1))^6+(x-sqr...

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  17. If the last tem in the binomial expansion of (2^(1/3)-1/(sqrt(2)))^n i...

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  18. The coefficient of x^(6) a^(-2) in the expansion of ((x^(2))/(a)-(a)/...

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  19. If in the expansion of (1 + ax)^(n),n in N, the coefficient of x an...

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  20. In the expansion of (x^3-1/(x^2))^n ,n in N , if the sum of the coeff...

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