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sum(r=1)^k(−3)^(r−1) .^(3n)C(2r−1)=0, wh...

`sum_(r=1)^k(−3)^(r−1) .^(3n)C_(2r−1)=0,` where `k=(3n)/2` and n is an even integer

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CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. Sum of last three digits of the number N=7^(100)-3^(100) is.

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  2. Let n be a positive integer and (1+x+x^2)^n=a0+a1x+ . . . . +a(2n)x^(2...

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  3. sum(r=1)^k(−3)^(r−1) .^(3n)C(2r−1)=0, where k=(3n)/2 and n is an even ...

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  4. The coefficient of the middle term in the binomial expansion in powers...

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  5. If in the expansion of (1+x)^n ,a ,b ,c are three consecutive coeffici...

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  6. If n and k are positive integers, show that 2^k( .^n C0)(.^n Ck)-2^(k-...

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  7. Prove that (25)^(n+1)-24n+5735 is divisible by (24)^2 for all n=1,2,.....

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  8. The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (a).(...

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  9. The coefficient x^5 in the expansion of (1+x)^(21)+(1+x)^(22)++(1+x)^...

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  10. If x^m occurs in the expansion (x+1//x^2)^(2n) , then the coefficient ...

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  11. If the coefficients of 5th, 6th , and 7th terms in the expansion of (1...

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  12. If (1+2x+x^2)^n=sum(r=0)^(2n)ar x^r ,then ar is a.(.^nC2)^2 b. .^n ...

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

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  14. If the coefficients of rth and (r+1)t h terms in the expansion of (3+7...

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  15. In the expansion of (1+3x+2x^2)^6 , the coefficient of x^(11) is a. 14...

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  16. If n-1Cr=(k^2-3)^nC(r+1), then (a) (-oo,-2] (b) [2,oo) (c) [-sqrt3, s...

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  17. Prove that (3!)/(2(n+3))=sum(r=0)^n(-1)^r((^n Cr)/(^(r+3)Cr))

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  18. If an=sum(r=0)^n1/(nCr), then sum(r=0)^n r/(nCr) equals

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  19. The expression (x+((x^3-1)^(1/2))/2)^5+""(x-((x^3-1)^(1/2))/2)^5 is a ...

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  20. Find ((dy) /dx) of sin(costheta) is

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