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Find the sum of the following C(0).C(3...

Find the sum of the following
`C_(0).C_(3)+C_(1).C_(4)+C_(2).C_(5)+…+C_(n-3).C_(n).`

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The correct Answer is:
`=""^(2n)C_((n+3))`
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Prove that following C_(0)+2.C_(1)+4.C_(2)+8.C_(3)+…+2^(n).C_(n)=3^(n)

Prove the following: C_(0)+(C_(2))/(3) +(C_(4))/(5) + … = (2^(n))/(n+1)

Prove that : For n = 0, 1, 2, 3, ………., n, prove that C_(0).C_(r)+C_(1).C_(r+1)+C_(2).C_(r+2)+….+C_(n-r).C_(n) =""^(2n)C_((n+r)) and hence deduce that C_(0).C_(1)+C_(1).C_(2)+C_(2).C_(3)+……..+C_(n-1).C_(n)=""^(2n)C_(n+1)

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Prove that C_0.C_3 + C_1.C_4 + C_2.C_5 + …..+C_(n-3).C_n = ""^(2n)C_(n +3)

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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-BINOMIAL THEOREM-TETUAL EXERCISES (EXERCISE - 6(a)) II.
  1. Find the numerically greatest term (s) in the expansion of (3+7x)^(n...

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  2. Prove that following i) 2.C(0)+5.C(1)+8.C(2)+…..+(3n+2)C(n)=(3n+4).2...

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  3. Prove that following C(0)-4.C(1)+7.C(2)-10.C(3)+……=0, if n is an eve...

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  4. Prove that following (C(1))/(2)+(C(3))/(4)+(C(5))/(6)+(C(7))/(8)+……=...

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  5. Prove that following C(0)+(3)/(2).C(1)+(9)/(3).C(2)+(27)/(4).C(3)+……...

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  6. Prove that following C(0)+2.C(1)+4.C(2)+8.C(3)+…+2^(n).C(n)=3^(n)

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  7. Find the sum of the following (""^(15)C(1))/(""^(15)C(0))+2(""^(15)C...

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  8. Find the sum of the following C(0).C(3)+C(1).C(4)+C(2).C(5)+…+C(n-3)...

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  9. Find the sum of the following 2^(2).C(0)+3^(2).C(1)+4^(2).C(2)+…..+(...

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  10. Find the sum of the following 3C(0)+6C(1)+12C(2)+…..+3.2^(n).C(n)

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  11. Using binomial theorem, prove that 50^(n)-49n-1 is divisible by 49^(2)...

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  12. Using binomial theorem, prove that 5^(4n)+52n-1 is divisible by 676 fo...

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  13. If (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+….+a(2n)x^(2n), then prove tha...

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  14. If (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+….+a(2n)x^(2n), then prove tha...

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  15. If (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+….+a(2n)x^(2n), then prove tha...

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  16. If (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+….+a(2n)x^(2n), then prove tha...

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  17. If (1+x+x^(2)+x^(3))^(7)=b(0)+b(1)x+b^(2)x^(2)+….b(21)x^(21), then fin...

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  18. If (1+x+x^(2)+x^(3))^(7)=b(0)+b(1)x+b^(2)x^(2)+….b(21)x^(21), then fin...

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  19. If the coefficient of x^(11) and x^(12) in the binomial expansion of (...

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  20. Find the remainder when 2^(2013) in divided by 17.

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