Here $\quad \mathrm{B}_{1}=\frac{\mu_{0} \mathrm{I}}{4 \pi \mathrm{a}}\left(\sin 30^{\circ}+\sin 30^{\circ}\right)$

$B_{1}=\frac{\mu_{0} I}{4 \pi a \cos 30^{\circ}}\left(\frac{1}{2}+\frac{1}{2}\right)$

$B_{1}=\frac{2 \mu_{0} I}{4 \sqrt{3} \pi a}$

Similarly, $\mathrm{B}_{2}=\frac{2 \mu_{0} \mathrm{I}}{8 \sqrt{3} \pi \mathrm{a}}$ and so on

$\therefore \quad \vec{\mathrm{B}}=\frac{2 \mu_{0} \mathrm{I}}{4 \sqrt{3} \pi \mathrm{a}}\left(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4} \ldots \ldots+\infty\right)$

$\vec{\mathrm{B}}=\frac{2 \mu_{0} \mathrm{I}}{4 \sqrt{3} \pi \mathrm{a}} \ln 2 \hat{\mathrm{k}}$

$\vec{\mathrm{B}}=\frac{\mu_{0} \mathrm{I}}{4 \sqrt{3} \pi \mathrm{a}} \ln 4 \hat{\mathrm{k}}$