Question

How do you find the sum of the infinite geometric series `4-8/3+16/9+...`?

Answer 1

Sum `=2.4`

Explanation:

Note that the ratio of successive terms (relative to the immediately preceding term) is `(-2/3)`

If
`{:(color(white)(-3/3)Sigma,=, 4-8/3+16/9-32/27+...), (underline(+2/3Sigma),=,underline(color(white)4+8/3-16/9+32/27-...)), (color(white)(+)5/3Sigma,=,4) :}`

`rArr Sigma = 4xx3/5= 2 2/4 = 2.4`