Question

1/(2根号1+1根号2)+1/(3根号2+2根号3)+.+1/(100根号99+99根号100)

Answer 1

1/(2根号1+1根号2)

=(2根号1-1根号2)/(4-2)

=根号1-(根号2)/2

1/(3根号2+2根号3)

=(3根号2-2根号3)/(18-12)

=(根号2)/2-(根号3)/3

1/(2根号1+1根号2)+1/(3根号2+2根号3)+.+1/(100根号99+99根号100)

=根号1-(根号)/2+(根号)/2-(根号3)/3+(根号)/3-...+(根号99)/99-(根号100)/100

=根号1-(根号100)/100

=1-1/10

=9/10