[" Let "a=(4^(1/401)-1)" and let "b_(n)=^(n)C_(1)+^(n)C_(2)*a+^(n)C_(3)*a^(2)+.........+^(n)C_(n)*a^(n)],[" Find the value of "(b_(2006)-b_(2005))]

Let a=(2^(1/401)-1) and for each n>=2, letb _(n)=^(n)C_(1)+^(n)C_(2)dot a+^(n)C_(3)a^(2)+......+^(n)C_(n)*a^(r). Find the value of (b_(2006)-b_(2005))

Let a=(2^(1//401)-1) and for each ngeq2,l e tb_n=^n C_1+^n C_2dota+^n C_3a^2+......+^n C_n*a^(n-1) . Find the value of (b_(2006)-b_(2005))dot

Let a=(2^(1//401)-1) and for each ngeq2,l e tb_n=^n C_1+^n C_2dota+^n C_3a^2+......+^n C_n*a^(n-1) . Find the value of (b_(2006)-b_(2005))dot

Let a=(2^(1//401)-1) and for each ngeq2,l e tb_n=^n C_1+^n C_2dota+^n C_3a^2+......+^n C_n*a^(n-1) . Find the value of (b_(2006)-b_(2005))dot

Let a=(4^(1/401)-1) and let b_n = nC_1 + nC_2 . a+ nC_3. a^2+......+ nC_n .a^(n-1). Find the value of (b_2006 – b_2005)

" Let "U_(n)=('^(n)C_(0))/(1)-('^(n)C_(1))/(5)+('^(n)C_(2))/(9)-.........((-1)^(n)'^(n)C_(n))/(4n+1)" and the value of "(4U_(99))/(U_(100))" is "

Let a=3^((1)/(223))+1 and for all >=3, let f(n)=^(n)C_(0)*a^(n-1)-^(n)C_(1)*a^(n-2)+^(n)C_(2)*a^(n-3)-...+(-1)^(n-1)*^(n)C_(n-1)*a If the value of f(2007)+f(2008)=3^(k)wherek in N, then the value of k is.

The value of (""^(n) C_(1)+2. ""^(n) C_(2)+3. ""^(n)C_(3)+…+ n""^(n)C_(n)) is-

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