Question

Is the geometric series `10 - 6 + 3.6 - 2.16 + ...` convergent or divergent?

Answer 1

Convergent series whose sum is `6.25`

Explanation:

In the series `10-6+3.6-2.16+....`

first term `a` is `10` and ratio `r` of a term and its preceding term is `-6/10=3.6/-6=-2.16/3.6=-0.6`

Hence it is a geometric series. If in such case `|r|<1`, the series is convergent and the sum of an infinite geometric series is given by

`a/(1-r)=10/(1-(-0.6))=10/1.6=(10xx10)/16=25/4=6.25`