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
S_{n}
= a(r^{n1})/(r1), if r >
1
or
S_{n}
= a(1r^{n})/(1r), 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/(1r).
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.
Winpossible's online math courses and tutorials have gained rapidly popularity since
their launch in 2008. Over 100,000 students have benefited from Winpossible's courses...
these courses in conjunction with free unlimited homework help serve as a very effective
mathtutor for our students.

All of the Winpossible math tutorials have been designed by topnotch instructors
and offer a comprehensive and rigorous math review of that topic.

We guarantee that any student who studies with Winpossible, will get a firm grasp
of the associated problemsolving techniques. Each course has our instructors providing
stepbystep solutions to a wide variety of problems, completely demystifying the
problemsolving process!

Winpossible courses have been used by students for help with homework and by homeschoolers.

Several teachers use Winpossible courses at schools as a supplement for inclass
instruction. They also use our course structure to develop course worksheets.