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Prove that .(r+1)*^n Cr-r*^n Cr+ ... +(-...

Prove that `.(r+1)*^n C_r-r*^n C_r+ ... +(-1)^r.^n C_r=(-1)^r.^(n-2)C_rdot`

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CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. Find the value of (sqrt(2)+1)^6-(sqrt(2)-1)^6dot

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  2. Using binomial theorem (without using the formula for .^n Cr) , prove ...

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  3. Prove that .(r+1)*^n Cr-r*^n Cr+ ... +(-1)^r.^n Cr=(-1)^r.^(n-2)Crdot

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  4. Find the sum .^n C0+^n C4+^n C8 + . . .

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  5. Find the value of ^4nC0+^(4n)C4+^(4n)C8++""^(4n)C(4n) .

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  6. Find the coefficient of x^n in the polynomial (x+^n C0)(x+3^n C1)xx(x+...

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  7. If (1+x)^(15)=C0+C1x+C2x^2++C(15)x^(15), then find the value of C2+2C...

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  8. Prove that (.^n C0)/1+(.^n C2)/3+(.^n C4)/5+(.^n C6)/7+ . . . =(2^n)/(...

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  9. Find the sum sumsum(0lt=ilt=jlt=n)^n Ci^n Cj

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  10. Find the sum sumsum(i!=j)^n ^nCi^n Cj

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  11. Show that the integer next above (sqrt(3)+1)^(2m) contains 2^(m+1) as ...

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  12. Prove that (1^2)/3""^n C1+(1^2+2^2)/5^n C2(1^1+2^2+3^2)/7^n C3+ +(1^2+...

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  13. Prove that 1/(n+1)=(.^n C1)/2-(2(.^n C2))/3+(3(.^n C3))/4- . . . +(-1^...

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  14. Find the sum 2C0+(2^3)/2C1+(2^3)/3C2+(2^4)/4C3++(2^(11))/(11)C(10)dot

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  15. If in the expansion of (2x+5)^(10) , the numerically greatest tem in ...

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  16. Find the value of 1/(81^n)-(10)/(81^n)^(2n)C1+(10^2)/(81^n)^(2n)C2-(10...

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  17. Find the value of 5C3 + 4C2

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  18. Find the sum 1C0+2C1+3C2++(n+1)Cn ,w h e r eCr=^n Crdot

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  19. If (1+x+x^2++x^p)^n=a0+a1x+a2x^2++a(n p)x^(n p), then find the value o...

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  20. If n >2, then prove that C1(a-1)-C2xx(a-2)++(-1)^(n-1)Cn(a-n)=a ,w h e...

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