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Prove that underset(r=0)oversetnsum3^r^n...

Prove that `underset(r=0)oversetnsum3^r^nC_r=4^n`

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A N EXCEL PUBLICATION-BINOMIAL THEOREM-QUESTION BANK
  1. Find(x+1)^6+(x-1)^6. Hence, or otherwise evaluate (sqrt2+1)^6+(sqrt2-1...

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  2. Show that 9^(n+1)-8n-9 is divisible by 64.

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  3. Prove that underset(r=0)oversetnsum3^r^nCr=4^n

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  4. Find the coefficient of x^5 in (x+3)^8.

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  5. Find the coefficient of a^5b^7 in the expansion of (a-2b)^12

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  6. Find the general term in the expansion of (x^2-y)^6.

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  7. Find the general term in the expansion of (x^2-yx)^12,x!=0

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  8. Find the 4th term in the expansion of (x-2y)^12

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  9. Find the 13^th term in the expansion of (9x-1/(3sqrtx))^18

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  10. Write the middle term in the expansion of the following, (3-x^3/6)^7

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  11. Find the middle term in the expansion of (x/3+9y)^10

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  12. In the expansion of (1+a)^(m+n), prove that the coefficient of a^m and...

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  13. The coefficients of the (r-1)^(th),r^(th) and (r+1)^(th) terms in the ...

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  14. Prove that the coefficient of x^n in the expansion of (1+x)^(2n) is ...

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  15. Find the positive value of m for which the coefficient of x^2 in the e...

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  16. Consider the expansion of (3x-x^3/6)^8 Find the general term in the ex...

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  17. Consider the expansion of (3x-x^3/6)^8 How many terms are there in the...

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  18. Consider the expansion of (3x-x^3/6)^8 Find the middle term in the exp...

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  19. Find the coefficient of middle term in the expansion of (1+a)^8

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  20. Find the coefficient of the middle term in the expansion of (1+a)^7

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