Find the sum of the following series to infinity : 10 – 9 + 8.1 –

1.	Find the sum of the following series to infinity : 10 – 9 + 8.1 – 7.29 + …. ∞
Answer» We observe that the above progression possess a common ratio. So it is a geometric progression. Common ratio = r = \(\frac{-9}{10}\) Sum of infinite GP = \(\frac{a}{1-r}\), Where a is the first term and r is the common ratio. Note : we can only use the above formula if \|r\|<1 Clearly, a = 10 and r = \(\frac{-9}{10}\) ⇒ sum = \(\frac{10}{1-(\frac{9}{10})}\)= \(\frac{100}{9}\)

Find the sum of the following series to infinity : 10 – 9 + 8.1 – 7.29 + …. ∞

Answer»

We observe that the above progression possess a common ratio. So it is a geometric progression. Common ratio = r = \(\frac{-9}{10}\)

Sum of infinite GP = \(\frac{a}{1-r}\), Where a is the first term and r is the common ratio.

Note : we can only use the above formula if |r|<1

Clearly, a = 10 and r = \(\frac{-9}{10}\)

⇒ sum = \(\frac{10}{1-(\frac{9}{10})}\)= \(\frac{100}{9}\)