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If Cr stands for nCr, then the sum of ...

If `C_r` stands for `nC_r`, then the sum of the series `(2(n/2)!(n/2)!)/(n !)[C_0^2-2C_1^2+3C_2^2-........+(-1)^n(n+1)C_n^2]` ,where n is an even positive integer, is

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CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
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  2. Find the coefficient of x^4 in the expansion of (x//2-3//x^2)^(10)dot

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  3. If Cr stands for nCr, then the sum of the series (2(n/2)!(n/2)!)/(n...

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  4. If the sum 1+2+2^2+......+2^(n-1)is 255, then find the number of ter...

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  5. The coefficient of X^24in the expansion of (1+X^2 )^12(1+X^12)(1+X^24)

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  6. Find the sum of the GP 1+3+9+27+........ 12terms

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  7. The coefficient of x^(53) in the expansion of sum(m=0)^(100) ^100Cm(x-...

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  8. The coefficient of the term independent of x in the expansion of [((x+...

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  9. In the expansion of (1+x+x^3+x^4)^10, the coefficient of x^4 is a..^...

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  10. If coefficient of a^(2)b^(3)c^(4) in (a+b+c)^(m) (where m in N) is L (...

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  11. The last two digits of the number 3^(400) are: (A) 81 (B) 43 (C) ...

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  12. The expression (sqrt(2x^2+1)+sqrt(2x^2-1))^6 + (2/(sqrt(2x^2+1)+sqrt(2...

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  13. A GP has common ratio 3, last term 486, if the sum of its terms is 728...

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  14. If (1+2x+3x^2)^(10)=a0+a1x+a2x^2+.....+a(20)x^(20),t h e na1 equals a....

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  15. Find the number of integral terms in the expansion of (5^(1/2)+7^(1/8)...

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  16. For which of the following values of x ,5t h term is the numerically g...

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  17. For natural numbers m ,n ,if(1-y)^m(1+y)^n=1+a1y+a2y^2+... , and a1=a2...

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  18. If the middle term in the expansion of (x/2+2)^8 is 1120, then find t...

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  19. If (1+x)^n=C0+C1x+C2x^2+...+Cn x^n , t h e n C0-(C0+C1)+(C0+C1+C2)-(C0...

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

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