15. Compute ln 2
We will use the formula
If we let x = 2, then x - 1 = 1 and we get
This will converge to ln 2. However, it converges very slowly. It is quicker to use the fact that
and if we use
taking the sum out one more term. Note that the negative outside the parentheses will turn all these terms positive. Converting to decimals we get
adding in the next term again. We see that we are getting closer and closer to the value we get of
that we get from a calculator.