Posted by **cecile** on Friday, January 4, 2008 at 5:51am.

find the sum of the infinite series (2/9)^2-(2/9)^3+(2/9)^4-(2/9)^5+ ...

- maths -
**Damon**, Friday, January 4, 2008 at 7:16am
(2/9)^2-(2/9)^3+(2/9)^4-(2/9)^5+

This is like a geometric series with the first terms missing

1 -1(2/9)^1 +1(2/9)^2-1(2/9)^3+(2/9)^4-(2/9)^5+

so if we find the sum of that series and subtract [1 -1(2/9)^1], we have it

so

g = 1

r = -2/9

in Sn = g (1-r^n)/(1-r)

n is infinite and |r| < 1

so Sn =g/(1-r)

Sn = 1/(1-2/9) = 1.286

so we want

1.286 -[1-2/9]

.508

- maths -
**Damon**, Friday, January 4, 2008 at 4:28pm
Whoa - typo

Sn = 1/(1+2/9) because r = -2/9

Sn = .818

so we want

.818 -[1-2/9]

.040

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