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

Find the sum `sumsum_(0lt=ilt=jlt=n)^n C_i^n C_j`

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If (1+x)^n=C_0+C_1x+C_2x^2+……..+C_nx^n then the value of sumsum_(0lt=iltjlt=n)C_iC_j is (A) 2^(2n-1)- .^(2n)C_(n/2) (B) .^(2n)C_n (C) 2^n (D) none of these

If (1+x)^n=C_0+C_1x+C_2x^2+.......+C_n x^n , then show that the sum of the products of the coefficients taken two at a time, represented by sumsum_(0lt=iltjlt=n) "^nc_i "^n c_j is equal to 2^(2n-1)-((2n)!)/ (2(n !)^2)

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CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. If (1+x)^(15)=C0+C1x+C2x^2++C(15)x^(15), then find the value of C2+2C...

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

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

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

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

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

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

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

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

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  11. Find the value of 5C3 + 4C2

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

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  13. 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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  14. 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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  15. Find the sum C0-C2+C4-C6+ ......... ,where Cr=^n Cr .

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

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  17. Find the sum 3 C1 + 5C2

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

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  19. 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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  20. If sum(r=0)^(2n)ar(x-2)^r=sum(r=0)^(2n)br(x-3)^ra n dak=1 for all kgeq...

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