Write out the terms of the series.
-$\sum_{\mathrm{i}=1}^{4} \frac{-\mathrm{x}^{\mathrm{i}}}{\mathrm{i}^{2}}$
A) $-x-\frac{x^{2}}{4}-\frac{x^{3}}{9}-\frac{x^{4}}{16}$

B) $-x-\frac{x^{2}}{2}-\frac{x^{3}}{3}-\frac{x^{4}}{4}$

C) $-x-4 x^{2}-9 x^{3}-16 x^{4}$

D) $-x+\frac{x^{2}}{4}-\frac{x^{3}}{9}+\frac{x^{4}}{16}$

Question

Write out the terms of the series.
-$\sum_{\mathrm{i}=1}^{4} \frac{-\mathrm{x}^{\mathrm{i}}}{\mathrm{i}^{2}}$
A) $-x-\frac{x^{2}}{4}-\frac{x^{3}}{9}-\frac{x^{4}}{16}$

B) $-x-\frac{x^{2}}{2}-\frac{x^{3}}{3}-\frac{x^{4}}{4}$

C) $-x-4 x^{2}-9 x^{3}-16 x^{4}$

D) $-x+\frac{x^{2}}{4}-\frac{x^{3}}{9}+\frac{x^{4}}{16}$

Quizplus · Accepted Answer

The series is defined as the sum of terms of the form $\frac{-x^i}{i^2}$ from $i=1$ to $i=4$. Substituting $i=1, 2, 3,$ and $4$ into the formula gives $-x-\frac{x^2}{4}-\frac{x^3}{9}-\frac{x^4}{16}$, which matches option A.