ਦਿਖਾਉ ਕਿ `(1xx2^2+2xx3^2+....+nxx(n+1)^2)/(1^2xx2+2^2xx3+...+n^2xx(n+1))=(3n+5)/(3n+1)`.

Show that (1xx2^2+2xx3^2+....+nxx(n+1)^2)/(1^2xx2+2^2xx3+...+n^2xx(n+1))=(3n+5)/(3n+1) .

Show that : (1 xx 2^2+2 xx 3^2+. .+n xx(n+1)^2)/(1^2 xx 2+2^2 xx 3+. .+n^2 (n+1)) =(3 n+5)/(3 n+1) .

Simplify: (2^-1xx2)/(2^2xx3^-4)^(7/2) xx (2^-2xx3^2)/(2^3xx3^-5)^(-5/2)

Simplify (16xx2^(n+1)-4xx2^n)/(16xx2^(n+2)-2xx2^(n+2))

If (9^n xx3^2xx(3^(n))-27^n)/(3^(3m)xx2^3)=1/27 , prove that m-n=1.

Find the value of (3^n × 3^(2n + 1))/(3^(2n) × 3^(n - 1))

lim_(n->oo)(1/(n^2+1)+2/(n^2+2)+3/(n^2+3)+....n/(n^2+n))

Give that : C_1+2C_2 x+3C_3 x^2+.....+2n. C_(2n). x^(2n-1)=2n(1+x)^(2n-1) , where C_r=((2n)!)/(r !(2n-r)!) , r=0,1,2, ,2n , then prove that C_1^2-2C_2^2+3C_3^2-..........-2n C_(2n)^2=(-1)^n . nC_n .