This is a free lesson from our course in Algebra II
In this section, you will walk through the steps explaining how to find the sum
for finite and infinite geometric series. The sum of the terms of a geometric progression is known as a geometric series. The sum of n terms of G. P., if the first
term is a and the common ratio is r is given by
Sn
= a(rn-1)/(r-1), if r >
1
or
Sn
= a(1-rn)/(1-r), if r <
1
For example, sum of 11 terms of G. P. 2, 4, 8, 16, ... is 4094.
(More text below video...)
(Continued from above)Another geometric series is S=1/91+1/637+1/4459+1/31213+... The common ratio is 1/7 in this case. A Geometric progression is often infinite. In other words, it has infinitely many elements.
The sum of infinite terms of G.P., when the first term is a and with the
common ratio is r(-1 < r < 1) approaches a real number.
Limits are used so that formula is handy for such a sum and it's given by
S = a/(1-r).
If |r| > 1, series diverges (goes to infinity) and sum does not exist. For example, sum of 11 terms of G. P. 2, 3/2, 9/8, 27/32, .........
is 8.
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is 8.