If `2^(n+4)-2^(n+2)=3` then n=

Prove that C_3 + 2.C_4+ 3.C_5 + ……..+ (n-2).C_n = (n-4).2^(n-1) + (n+2) where n > 3

If S_(n) = sum_(n=1)^(n) (2n + 1)/(n^(4) + 2n^(3) + n^(2)) then S_(10) is less then

If (n !)/(2!(n-2)!) and (n !)/(4!(n-4)!) are in the ratio 2:1 , find the value of ndot

The value of (2^(n+4)-2*2^(n))/(2.2^(n+3))+2^(-3)

(i) If (n!)/(2.(n-2)!): (n!)/(4!.(n-4)!) = 2:1 , find the valye of n. (ii) If ((2n)!)/(3!(2n-3)!): (n!)/(2!(n-2)!) = 44:3 , then find the value of n.

If a != 1 and l n a^(2) + (l n a^(2))^(2) + (l n a^(2))^(3) + ... = 3 (l n a + (l n a)^(2) + ( ln a)^(3) + (l n a)^(4) + ....) then 'a' is equal to

If S=sum_(n=2)^(oo) (3n^2+1)/((n^2-1)^3) then 9/4Sequals

If (1+a)^(n)=.^(n)C_(0)+.^(n)C_(1)a+.^(n)C_(2)a^(2)+ . . +.^(n)C_(n)a^(n) , then prove that .^(n)C_(1)+2.^(n)C_(2)+3.^(n)3C_(3)+ . . .+n.^(n)C_(n)=n.2^(n-1) .

Find the value of n in each of the following: (2^2)^n=(2^3)^4 (ii) 2^(5n)-:2^n=2^4 (iii) 2^n^(-5)xx5^n^(-4)=5

If S_(n)=(1^(2).(2))/(1!)+(2^(2).3)/(2!)+(3^(2).4)/(3!)+…(n^(2).(n+1))/(n!) then lim_(n rarr infty) S_(n) is equal to