(1times2^(2)+2times3^(2)+...+n(n+1)^(2))/(1^(2)times2+2^(2)times3+...+n^(2)times(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) xx (n + 1)) = (3n + 5)/(3n + 1)

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

(5^(n+3)-6times5^(n+1))/(9times5^(n)-2^(2)times5^(n))

(2^(n+3)-10times2^(n+1))/(2^(n+1)times6)=

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) .

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)

lim_(x->oo) [(1)/(1times2)+(1)/(2times3)+(1)/(3times4)+.....+(1)/(n(n+1))]

(9^(n)times3^(2)times3^(n)-(27)^(n))/((3^(3))^(5)times2^(3))=(1)/(27)," find the value of "n