[lim_(n rarr oo)[(1)/(n^(2))sec^(2)(1)/(n^(2))+(2)/(n^(2))sec^(2)(4)/(n^(2))+cdots(1)/(n^(2))sec^(2)1]" equals "],[[" (a) "tan1," (b) "tan1],[" (c) "(1)/(2)sec1," (d) "(1)/(2)cosec1]]

Evaluate: lim_(n rarr oo)[(1)/(n^(2))sec^(2)(1)/(n^(2))+2/n^(2)sec^(2)(4)/(n^(2))+...+(1)/(n)sec^(2)1]]

{:(" "Lt),(n rarr oo):} [ (1)/(n^(2)) sec^(2). (1)/(n^(2)) + (2)/(n^(2))sec^(2). (4)/(n^(2))+...+1/n sec^(2)1]=

Definite integration as the limit of a sum : lim_(ntooo)[(1)/(n^(2))sec^(2)""(1)/(n^(2))+(2)/(n^(2))sec^(2)""(4)/(n^(2))+.......+(1)/(n)sec^(2)1] a. 'tan1 b. 1/2tan1 c. 1/2sec1 d. 1/2cosec 1

lim_(n rarr oo) sum_(r=1)^(n) r/n^(2) sec^(2) (r^(2)/n^(2)) =

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

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