If `A_n` is the area bounded by `y=xa n dy=x^n ,n in N ,t h e nA_2dotA_3 A_n=` `1/(n(n+1))` (b) `1/(2^nn(n+1))` `1/(2^(n-1)n(n+1))` (d) `1/(2^(n-2)n(n+1))`

((n+2)!+(n+1)(n-1)!)/((n+1)(n-1)!)=

lim_(n rarr oo)((n^(2)-n+1)/(n^(2)-n-1))^(n(n-1)) is

underset(n to oo)lim ((n^(2)-n+1)/(n^(2)-n-1))^(n(n-1))

If A_n be the area bounded by the curve y=(tanx^n) ands the lines x=0,\ y=0,\ x=pi//4 Prove that for n > 2. , A_n+A_(n+2)=1/(n+1) and deduce 1/(2n+2)< A_(n) <1/(2n-2)

Prove that ((2n+1)!)/(n!)=2^(n){1.3.5(2n-1)(2n+1)}

If n in N, n > 1 , then value of E= a - ""^(n)C_(1) (a-1) + ""^(n)C_(2) (a -2)+ ... + (- 1)^(n) (a-n) (""^(n)C_(n)) is

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))

Prove that (1)/(n!)+(1)/(2!(n-2)!)+(1)/(4!(n-4)!)+...=(1)/(n!)2^(n-1)

If y=x^(2)e^(x) ,show that y_(n)=(1)/(2)n(n-1)y_(2)-n(n-2)y_(1)+(1)/(2)(n-1)(n-2)}