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Expand the series for \(\ln(1+x)=\displaystyle\sum_{k=1}^\infty \frac{(-1)^{k-1} x^k}{k}\) up to the term of order 4.
\(\ln(1+x)=\)
\(+\displaystyle\sum_{k=5}^\infty \frac{(-1)^{k-1} x^k}{k}\)