INFINITE GEOMETRIC SERIES

Front

What is an infinite geometric series?

Back

An infinite geometric series is the sum of the terms of a geometric sequence that continues indefinitely. It converges if the absolute value of the common ratio is less than 1.

Front

What is the formula for the sum of an infinite geometric series?

Back

The sum S of an infinite geometric series with first term a and common ratio r (|r| < 1) is given by: S = a / (1 - r).

Front

Given the first term 318 and common ratio 1/2, what is the sum of the infinite geometric series?

Back

The sum is 636.

Front

Evaluate the infinite geometric series: 3 - 2 + 4/3 - 8/9 + ...

Back

The sum is 9/5.

Front

Back

The sum is 5.

Front

What does it mean if a geometric series diverges?

Back

A geometric series diverges if the absolute value of the common ratio is greater than or equal to 1, meaning the sum does not approach a finite limit.

Front

Find the sum of the infinite geometric series: 200 - 100 + 50 - 25 + ...

Back

The sum is 400/3.

Front

What is the common ratio in the series 3 - 2 + 4/3 - 8/9 + ...?

Back

The common ratio is -2/3.

Front

If the first term of a geometric series is 5 and the common ratio is 1/3, what is the sum?

Back

The sum is 5 / (1 - 1/3) = 7.5.

Front

Back