" 93."((2^(n)+2^(n-1)))/((2^(n+1)-2^(n)))

If A=([x,x],[x,x]) then A^(n)(n in N)= 1) ([2^nx^n,2^nx^n],[2^nx^n,2^nx^n]) 2) ([2^(n-1) x^n,2^(n-1) x^n],[2^(n-1) x^n,2^(n-1) x^n]) 3) I 4) ([2^(n) x^(n-1),2^(n) x^(n-1)],[2^(n) x^(n-1),2^(n) x^(n-1)])

Divide x^(2n)+a^(2^(n-1))x^(2^(n-1))+a^(2^(n))byx^(2^(n-1))-a^(2^(n-2))x^(2^(n-2))+a^(2^(n-1))

If S_(n)=sum_(r=1)^(n)(1+2+2^(2)+......+2^(r))/(2^(r)), then S_(n) is equal to (a)2^(n)n-1( b) 1-(1)/(2^(n))(c)2n-1+(1)/(2^(n))(d)2^(n)-1

Evaluate: ("lim")_(nvecoo)n^(-n^2){(n+2^0)(n+2^(-1))(n+2^(-2))(n+2^(-n+1))}^n

Find the sum of series upto n terms ((2n+1)/(2n-1))+3((2n+1)/(2n-1))^(2)+5((2n+1)/(2n-1))^(3)+

The coefficient of 1/x in the expansion of (1+x)^(n)(1+1/x)^(n) is (n!)/((n-1)!(n+1)!) b.((2n)!)/((n-1)!(n+1)!) c.((2n-1)!(2n+1)!)/((2n-1)!(2n+1)!) d.none of these

If n is a positive integer, prove that 1-2n+(2n(2n-1))/(2!)-(2n(2n-1)(2n-2))/(3!)++(-1)^(n-1)(2n(2n-1)(n+2))/((n-1)!)=(-1)^(n+1)(2n)!//2(n !)^2dot

If n is a positive integer, prove that 1-2n+(2n(2n-1))/(2!)-(2n(2n-1)(2n-2))/(3!)++(-1)^(n-1)(2n(2n-1)(n+2))/((n-1)!)=(-1)^(n+1)(2n)!//2(n !)^2dot

(1^(2))/(1.3)+(2^(2))/(3.5)+(3^(2))/(5.7)+.....+(n^(2))/ ((2n-1)(2n+1))=((n)(n+1))/((2(2n+1)))

Show : 2^(n)-(n)/(1!).2^(n-1)+(n(n-1))/(2!).2^(n-2)-....+(-1)^(n)=1