If my heigth is increasing 1/2 today, 1/3 the next day, 1/4 the next day and so on, what is the smallest days that my heigth will be 100times than my original height?

Answer 1

a close estimate is the integral of dx/x= 1/2+1/3+1/4+1/5+....+1/x

= lnx evaluated from 1 to x

=100. solve for x

lnx = 100

put both sides over base e

e^lnx = e^100

x = e^100

use a calculator

= about 2.688117142 x 10^43 days