" 7."lim_(n rarr oo)(1+(1)/(2)+(1)/(4)+....+(1)/(2^(n)))/(1+(1)/(3)+(1)/(9)+...+(1)/(3^(n)))=

lim_(n rarr oo)(2^(n)+3^(n))^(1/n)

lim_(n rarr oo)((1)/(1.4)+(1)/(4.7)++(1)/((3n-2)(3n+1))))

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

lim_(n rarr oo)[(1)/(n)+(1)/(n+1)+(1)/(n+2)+.....+(1)/(2n)]

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

lim_(n rarr oo){(1)/(1.3)+(1)/(3.5)+(1)/(5.7)+....+(1)/((2n+1)(2n+3 ))

lim_(n rarr oo) ((1)/(1.2) + (1)/(2.3) + (1)/(3.4) +…..+ (1)/(n(n+1))) is :

lim_ (n rarr oo) ((1) / (3) + (1) / (3 ^ (2)) + (1) / (3 ^ (3)) ++ (1) / (3 ^ (n) ))

lim_ (n rarr oo) [(1+ (1) / (n)) (1+ (2) / (n)) (1+ (n) / (n))] ^ ((1) / (n) )