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Sum of the terms of an infinite PG


Consider an unlimited PG (infinite terms) and decreasing. Under these conditions we can consider that at the limit we will have theno = 0. Substituting in the previous formula, we will find:

For example, solve the equation:

x + x / 2 + x / 4 + x / 8 + x / 16 +… = 100

The first member is a first term PG x and ratio 1/2. So, substituting in the formula, comes:

From this equation we find as answer x = 50.

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