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

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

(6^(n+3)-32*6^(n+1))/(6^(n+2)-2*6^(n+1))=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

sqrt(m^(2)n^(2))times root(6)(m^(2)n^(2))times root(3)(m^(2)n^(2))

Simplify the following: (i)\ (5^(n+3)-\ 6\ xx\ 5^(n+1))/(9\ xx\ 5^n-2^2\ xx\ 5^n) (ii)\ (6(8)^(n+1)+\ 16(2)^(3n-2))/(10(2)^(3n+1)-7\ (8)^n)

Simplify (6(8)^(n+1)+16(2)^(3n-2))/(10(2)^(3n+1)-7(8)^(n))

Evaluate : (a^(2n+1) xx a^((2n+1)(2n-1)))/(a^(n(4n-1)) xx (a^2)^(2n+3)