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If the first three terms in the expansio...

If the first three terms in the expansion of `(1+ax)^n` are `1,-21x` and `216x^2` respectively, prove that `a=-3/7` and n=49.

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A N EXCEL PUBLICATION-BINOMIAL THEOREM-QUESTION BANK
  1. Consider the expansion of (x+a)^n If these are 112,7 and 1/4 respectiv...

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  2. Expand (1+ax)^n upto the third term if n is a positive integer

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  3. If the first three terms in the expansion of (1+ax)^n are 1,-21x and 2...

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  4. What is the coefficient of the (r+1)^(th) term in the expansion of (1+...

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  5. What is the coefficient of 5th, 6th and 7th terms in the expansion of ...

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  6. If they are in A.P, find the possible values of n

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  7. Expand 2^(3n) by writing 2^(3n)=(1+7)^n

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  8. Using binomial theorem prove that 2^(3n)-7n-1 is divisible by 49, wher...

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

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

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

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

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

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

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

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

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

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

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

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

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