# Math Help - analysis 4.1.3

1. ## analysis 4.1.3

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?

2. Originally Posted by pila0688
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?
$R_N=\left|S-S_n\right|\leq{a_{N+1}}$

Therefore you just need to solve $\frac{1}{N+1}\leq{C}$ where $C$ is the desired accuracy.