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If x+y=1, prove that sum(r=0)^n .^nCr x^...

If `x+y=1,` prove that `sum_(r=0)^n .^nC_r x^r y^(n-r) = 1`.

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CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. If n gt 2, then prove that C(1)(a-1) - C(2) xx (a-2) + "….." + (-1)^(...

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  2. Find the sum C0-C2+C4-C6+ ......... ,where Cr=^n Cr .

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  3. If x+y=1, prove that sum(r=0)^n .^nCr x^r y^(n-r) = 1.

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  4. Find the sum 3 C1 + 5C2

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  5. Prove that (.^(n)C(1))/(2) + (.^(n)C(3))/(4) + (.^(n)C(5))/(6) + "…." ...

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  6. If (1+x)^n=sum(r=0)^n^n Cr , show that C0+(C1)/2++(Cn)/(n+1)=(2^(n+1...

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  7. If underset(r=0)overset(2n)suma(r) (x-2)^(r) = underset(r=0)overset(2n...

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  8. 3^(2n+2)-8n-9 is divisible by

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  9. Statement 1: The number of distinct terms in (1+x+x^2+x^3+x^4)^(1000) ...

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  10. The product of 3rd and 8th term of a GP is 243. If its 4th term is 3. ...

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  11. The value of "^30C0.^30C10+^30C1.^30C11+^30C2.^30C(12)+……+^30C(20) . ^...

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  12. If f(x)=x^n ,f(1)+(f^1(1))/1+(f^2(1))/(2!)+........(f^n(1))/(n !),w h ...

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  13. The fractional part of =(2^(4n))/15 is

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  14. The value of .^(15)C(0)^(2)-.^(15)C(1)^(2)+.^(15)C(2)^(2)-"...."-.^(15...

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  15. If the sum of the coefficients in the expansion of (1-3x+10 x^2)^ni sa...

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  16. If (1+x-2x^2)^6=1+a1x+a2x^2+……+a(12)x^12 then

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  17. Maximum sum of coefficient in the expansion of (1-xsintheta+x^2)^n is

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  18. If the sum of the coefficients in the expansion of (a+b)^(n) is 4096, ...

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  19. The number of distinct terms in the expansion of (x+1/x+x^2+1/(x^2))^(...

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  20. The sum of the coefficients of even power of x in the expansion of (1+...

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