An infinite geometric series is a series of the form
a + ar + ar² + ar³ + ar⁴ + ...
The sum of an infinite geometric series:
Sn= a + ar + ar² + ar³ + ar⁴ + ...
a + r (a + ar + ar² + ar³ + ar⁴ + ...)
a + rS
Solve the equation S= a + rS for S
S - rS = a
(1 - r)S = a
a
S= 1 - r , for -1 < r < 1.
if -1 < r < 1 for theses values of r, Sn has no limit or no sum.
Illustrative Examples:
Direction: Determine if each infinite geometric series has a sum. If the sum exists, find the sum.
1.) -5 + (-0.5) + (-0.05) + (-0.005) + ...
a= 5
r= 0.1
a -5 -5
Sn= 1 - r = 1 - 0.1 = 0.9 = -5.55 or 5.5
2.) 16 + 8 + 4 + 2 + ...
a= 16
r= ½
a 16 16
Sn= 1 - r = 1 - ½ = ½ = 8
3.) 1 + ⅓ + 1/9 + 1/27 + ...
a= 1
r= 3
a 1 1
Sn= 1 - r = 1- 2 = 1 = 1
A/N: I'm back after death. Also, I already told you that I'm already grade 11. I took the HUMSS strand and I have a complete notes of one of our subject Earth and Life science. Should I transfer it here in wattpad? Just so I could help ':))
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MATHEMATICS 10
Non-FictionThis book contains topics from Grade 10 Mathematics. This book might not have all the topics of Mathematics in grade 10 but it will surely help you. Use this as a guide to your Math subject but don't always depend here. Date created: May 8, 2019 Da...
