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Prove that sum(r=0)^(2n)(r. ^(2n)Cr)^2=n...

Prove that `sum_(r=0)^(2n)(r. ^(2n)C_r)^2=n^(4n)C_(2n)` .

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CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
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  2. Find the sum sum(i=0)^r.^(n1)C(r-i) .^(n2)Ci .

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  3. Prove that sum(r=0)^(2n)(r. ^(2n)Cr)^2=n^(4n)C(2n) .

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  4. If k a n d n are positive integers and sk=1^k+2^k+3^k++n^k , then prov...

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  5. Prove that sum(r=1)^n(-1)^(r-1)(1+1/2+1/3++1/r)^n Cr=1/n .

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  6. Prove that (C1)/1-(C2)/2+(C3)/3-(C4)/4++((-1)^(n-1))/n Cn=1+1/2+1/3++1...

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  7. Prove that sum(r=0)^n^n Crsinr xcos(n-r)x=2^(n-1)sin(n x)dot

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  8. Find the last two digits of the number (23)^(14)dot

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  9. Find the last two digits of the number 27^(27)dot

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  10. Find the number of nonzero terms in the expansion of (1+3sqrt(2)x)^9+(...

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

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

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

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

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

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