मान ज्ञात कीजिए :
`Lim_(ntooo) [(1)/(n^(2))sec ^(2)"" (1)/(n^(2))+(2)/(n^(2))sec ""^(2) ""(4)/(n^(2))+(3)/(n^(2))sec ^(2)""(9)/(n^(2))+...+ 1/n sec ^(2)1].`

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))]

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]=

lim_(n to oo) [1/(n^2) "sec"^2 1/(n^2) + 2/(n^2) "sec"^(2) 4/(n^2) + …… + 1/n "sec"^(2) 1] equals :

Lt_(ntooo)(1)/(n)[sec^(2)""(pi)/(4n)+sec^(2)""(2pi)/(4n)+......+sec^(2)""(npi)/(4n)]=

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

Evaluate lim_(ntooo) (1)/(1+n^(2))+(2)/(2+n^(2))+...+(n)/(n+n^(2)).