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)(r^(n)-1)/(r-1)\\\\S_(10)=4\cdot ((-(1)/(2))^(10)-1)/(-(1)/(2)-1)=4\cdot (((1)/(1024)-1))/((-(3)/(2)))\\\\=(8)/(3)\cdot (1023)/(1024)=(341)/(128)`

The sum is approximately 2.66.