![]() We can consider what happens with our convergent geometric series as □ approaches infinity. In other words, if | □ | <</a> 1, then l i m → ∞ □ = 0. This means that as □ approaches infinity, □ must approach zero.
We stated earlier that for a convergent geometric series, − 1 < □ < 1. ĭividing both sides of this equation by 1 − □, we derive the formula for the sum of the first □ terms of a geometric series with first term □ and common ratio □: □ = □ ( 1 − □ ) 1 − □. Notice that when we subtract the terms on the right-hand side, most of the terms become zero: □ − □ □ = □ − □ □ □ ( 1 − □ ) = □ ( 1 − □ ). We
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