`Lim_(n->oo)[1/n^2 * sec^2 (1/n^2)+2/n^2 * sec^2 (4/n^2)+..............+1/n * sec^2 1]`

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]

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]]

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

lim_ (n rarr oo) (pi) / (6n) [sec ^ (2) ((pi) / (6n)) + sec ^ (2) (2 * (pi) / (6n)) + .... ..... + sec ^ (2) ((n-1) (pi) / (6n)) + (4) / (3)]

lim_(n to oo) [ 1^2/n^3 + (2^2)/(n^3) + …+ ((n-1)^2)/(n^3)]

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

lim_(n rarr oo)[(1)/(n^(2))sec^(2)((pi)/(3n^(2)))+(2)/(n^(2))sec^ (2)((4 pi)/(3n^(2)))+(3)/(n^(2))sec^(2)((9 pi)/(3n^(2)))+. .....+(1)/(n)sec^(2)((pi)/(3))]