Im trying to solve a question that is similar to this one, so any help with this one will be greatly appreciated. I know that the final answer is 84 terms.

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> Consider the Taylor expansion:
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> > $$ln(1+x)=x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+...$$
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> Estimate how many terms are required to obtain $ln(\frac{31}{16})$ to four decimal places accuracy.
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I've started off so far by saying $$ln(1+x)=\sum\_{n=1}^\infty(-1)^{n+1}\frac{x^n}{n}$$
and
$$(1+x)= \frac{31}{16} \text{ so }x=\frac{15}{16}$$

Thanks in advance.