Question

Find the sum of the infinite series if it exists. If it exists, round to one decimal place. If it does not exist, write none. 4 + 3.2 + 2.56 + 2.048

Answer 1

4*0.8 = 3.2
3.2*0.8 = 2.56
2.56*0.8 = 2.048

Answer 2

thank you so much

Answer 3

0.8

Answer 4

np

Answer 5

I don't think we have the question answered yet. We have identified the series, but didn't find the sum. We can consider it this way\[\sum_{k=0}^{\infty} 4(\frac{4}{5})^k=4\sum_{k=0}^{\infty}(\frac{4}{5})^k=\frac{4}{1-\frac{4}{5}}=20\]The last bit comes from a relationship\[\sum_{k=0}^{\infty} r^k=\frac{1}{1-r}~~~0<r<1\]