Prove that (.^(2n)C0)^2-(.^(2n)C1)^2+(.^...

Prove that `(.^(2n)C_0)^2-(.^(2n)C_1)^2+(.^(2n)C_2)^2-..+(.^(2n)C_(2n))^2` = `(-1)^n.^(2n)C_n`.

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

Prove that .^(n)C_(0) - .^(n)C_(1) + .^(n)C_(2) - .^(n)C_(3) + "……" + (-1)^(r) .^(n)C_(r) + "……" = (-1)^(r ) xx .^(n-1)C_(r ) .

Prove that .^(n)C_(1) + 2 xx .^(n)C_(2) + 3 xx .^(n)C_(3) + "…." + n xx .^(n)C_(n) = n2^(n-1) . Hence, prove that .^(n)C_(1).(.^(n)C_(2))^(2).(.^(n)C_(3))^(3)"......."(.^(n)C_(n))^(n) le ((2^(n))/(n+1))^(.^(n+1)C_(2)) AA n in N .

Prove that .^(n)C_(0) + (.^(n)C_(1))/(2) + (.^(n)C_(2))/(3) + "……" +(. ^(n)C_(n))/(n+1) = (2^(n+1)-1)/(n+1) .

Prove that ^nC_0 "^(2n)C_n-^nC_1 ^(2n-2)C_n +^nC_2 ^(2n-4)C_n =2^n

The value of the sum (.^(n)C_(1))^(2)+(.^(n)C_(2))^(2)+(.^(n)C_(3))^(2)+....+(.^(n)C_(n))^(2) is -

Prove that, C_(0)^(2)+C_(1)^(2)+C_(2)^(2)+.......+C_(n)^(2)=((2n)!)/(n!)^(2)

.^(n)C_(r)+2.^(n)C_(r-1)+.^(n)C_(r-2)=.^(n+2)C_(r)(2lerlen) .

Prove that .^(n)C_(0) +5 xx .^(n)C_(1) + 9 xx .^(n)C_(2) + "…." + (4n+1) xx .^(n)C_(n) = (2n+1) 2^(n) .

Prove that sum_(r=0)^(2n) r.(""^(2n)C_(r))^(2)= 2n.""^(4n-1)C_(2n-1) .

CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions

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Find the sum C0+3C1+3^2C2+...+3^n Cndot
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