Question

Evaluate the series 4 – 2 + 1 – 0.5 + 0.25 to S10. Round to the nearest hundredth.

Answer 1

The initial term of this geometric series is 4, and the common ratio is -1/2. The sum is given by

$S_{n}=a_{1}\dfrac{r^{n}-1}{r-1}\\\\S_{10}=4\cdot \dfrac{(-\frac{1}{2})^{10}-1}{-\frac{1}{2}-1}=4\cdot \dfrac{(\frac{1}{1024}-1)}{(-\frac{3}{2})}\\\\=\dfrac{8}{3}\cdot \dfrac{1023}{1024}=\dfrac{341}{128}$

The sum is approximately 2.66.