on description hehehs

Question

Given the infinite geometric series: 7-2.8+1.12-0.448+...

1. What is the particular value that the sums are approaching?

Answer 1

The series 7 - 2.8 + 1.12 - 0.448 + ... is geometric with common ratio r = 0.4

S_n = sum of first n terms

S = lim_n→∞S_n = sum of the entire series

Since r is in the interval (-1,1), S is finite and is equal to a / (1-r), where a is the first term of the series.

So S = 7 / (1-0.4) = 11 2/3