[p^(TT)T],[2^(n)>1+n*sqrt(2^(n-1))n>1]

Lt_(ntooo)[(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+(1)/(sqrt((2n-1)))]=

lim_(nto oo)1/n+(1)/(sqrt(n^(2)+n))+(1)/(sqrt(n^(2)+2n))+...(1)/(sqrt(n^(2)+(n-1)n)) is equal to

Lt_(n rarr oo)[(1)/(n)+(1)/(sqrt(n^(2) -1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+... "to n terms"]

If the major axis is n times the minor axis of the ellipse,then eccentricity is 1) (sqrt(n-1))/(n) 2) (sqrt(n-1))/(n^(2)) 3) (sqrt(n^(2)-1))/(n^(2)) 4) (sqrt(n^(2)-1))/(n)

If (1-sqrt(2))^(n),1,(1+sqrt(2))^(n) are in G.P., then n can be

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

Definite integration as the limit of a sum : lim_(ntooo)[(1)/(n)+(1)/(sqrt(n^(2)+n))+(1)/(sqrt(n^(2)+2n))+.......+(1)/(sqrt(n^(2)+(n-1)n))]=.........

lim_(nrarroo) [(1)/(n)+(sqrt(n^(2)-1^(2)))/(n^(2))+(sqrt(n^(2)-2^(2)))/(n^(2))+...+(sqrt(n^(2)-(n-1)^(2)))/(n^(2))]

underset(nrarroo)lim[(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+(1)/(sqrt(n^(2)-3^(2)))+...+(1)/(sqrt(n^(2)-(n-1)^(2)))]

lim_(nrarroo) {(1)/(sqrt(n^(2)))+(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+...+(1)/(sqrt(n^(2)-(n-1)^(2)))} is equal to-