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The process of seeking limit in freshman mathematics
lim(n->; ∞)∑(I: 1-& gt; √(n^2-i^2 /n^2

= lim(n->; ∞) ( 1/n)∑(i: 1->n) √( 1-(i/n)^2)

=∫(0-& gt; √( 1-x^2) dx

=π/4

let

x=sinu

dx=cosu du

x=0,u=0

x= 1,u=π/2

∫(0->; √( 1-x^2) dx

=∫(0->; π/2) (cosu) du

=( 1/2)∫(0->; π/2) ( 1+cos2u) du

=( 1/2)[u+( 1/2)sin2u]|(0-& gt; π/2)

=π/4