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Prove that ""^(n+1)C(r+1)=(n+1)/(r+1)"^n...

Prove that `""^(n+1)C_(r+1)=(n+1)/(r+1)"^nC_r`

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Prove that nC_r = nC_(n-r)

Prove that ""^(n)C_(0)""^(n)C_(0)-^(n+1)C_(1) ""^(n)C_(1)+^(n+2)C_(2)""^(n)C_(2)....=(-1)^(n)

Prove that (""^nP_r)/(""^nC_r)=r!

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A N EXCEL PUBLICATION-BINOMIAL THEOREM-QUESTION BANK
  1. Using binomial theorem prove that 2^(3n)-7n-1 is divisible by 49, wher...

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  2. prove the result ^(n+1)Cr=^nC(r-1)+^nCr

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  3. Prove that ""^(n+1)C(r+1)=(n+1)/(r+1)"^nCr

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  4. Prove that (C0+C1)(C1+C2)(C2+C3)...(C(n-1)+Cn)=(C0C1C2...C(n-1)(n+1)^n...

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  5. Prove that ""^(n+1)C(r+1)=(n+1)/(r+1)"^nCr

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  6. Prove that C0+C2/3+C4/5+...=(2^n)/(n+1)

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  7. Given that Cr/(C(r-1))=(n-r+1)/r Evaluate C1/C0,C2/C1 and C3/C2

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  8. Given that Cr/(C(r-1))=(n-r+1)/r Prove that (1+C1/C0)(1+C2/C1)...(1+C...

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  9. Given that C0+C1x+C2x^2+..+Cnx^n=(1+x)^n prove that C0+5.C1+5^2.C2+......

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  10. Given that C0+C1x+C2x^2+..+Cnx^n=(1+x)^n Prove that C(1).2+C(2).2^2+....

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  11. Find the coefficient of x^4 in the expansion of (1+x)^n(1-x)^n

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  12. Find the coefficient of x^4 in the expansion of (1-x^2)^n

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  13. What is the value of C0+C1+C2+..+Cn?

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  14. What is the value of C0+C2+C4+....?

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  15. What is the value of C1+C3+C5+...?

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  16. Prove that 2C0+C1+2C2+C3+2C4+...=3.2^(n-1)

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  17. What is the coefficient of x^(n-2) in the expansion of (1+x)(1+x)^n?

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  18. What is the coefficient of x^(n-2) in the expansion of (1+x)^(2n)?

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  19. Prove that C0C2+C1C3+…+C(n-2)Cn=^(2n)C(n-2)

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  20. Given that 1/(r+1)""^nCr=1/(n+1)"'^(n+1)C(r+1) Prove that 2""^10C0+2^...

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