A term in geometric series is formed by multiplying the previous term by a constant - which is called the common ratio.
For example, the series 2, 4, 8, 16, 32, ... has a common ratio of 2.
1. Find x if 5 + x + 45 + ... is a geometric series.
2. Is a geometric series?
In some geometric series, the sum becomes very large as n increases. This series diverges, or it has an infinite sum. However, some geometric series has a limiting sum, that is, there is a limit to the sum of all of the terms in the series up to infinity-th term. Yes, infinity! This series converges and has a limiting sum.
For example, the series , notice that after a while the terms are becoming closer and closer to zero and so will not add much to the sum of the whole series. Estimate its limiting sum.
For , as n increases, decreases and approaches zero e.g. when .
Using the example above,