Problem $4\mathrm{.}2\mathrm{.}1.$ Use the fact that

$1-(1)/(2)+(1)/(3)-$cdots$+((-1)^(2$k$+1))/(2$klncdots$+((-1)^(2$k$+2))/(2$k$+1)$

to determine how many terms of the series $\backslash$sum$\_($n$=1)^(\backslash$infty $)((-1)^($n$+1))/($n$)$ should be added

together to approximate ln$2$ to within $\mathrm{.}0001$ without actually computing what

ln$2$ is$.$