how many terms of the series 1-1/2+1/3-1/4+... do we need to take if we are to guarantee that we have an approximation to the target value, ln2, with 10-digit accuracy? with 20-digit accuracy? with 100-digit accuracy?
how many terms of the series 1-1/2+1/3-1/4+... do we need to take if we are to guarantee that we have an approximation to the target value, ln2, with 10-digit accuracy? with 20-digit accuracy? with 100-digit accuracy?
Therefore you just need to solve where is the desired accuracy.