Прогрессии : Арифметическая прогрессия и геометрическая прогрессия


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Арифметическая прогрессия

1. Если  есть n-ый член арифметической прогрессии, d - разность, а - сумма n первых членов арифметической прогрессии, то

Арифметическая прогрессия возрастает, если d>0, и убывает, если d<0.

2. Каждый член арифметической прогрессии, отличный от первого и последнего, равен среднему арифметическому соседних с ним членов:

3.

где

 Геометрическая прогрессия

1. Если есть n-ый член геометрической прогрессии, q - разность, а - сумма n первых членов геометрической прогрессии, то

2. Квадрат каждого члена геометрической прогрессии, отличного от первого и последнего, равен произведению соседних с ним членов:

3.

где  

Бесконечно убывающая геометрическая прогрессия

Если S есть сумма бесконечно убывающей геометрической прогрессии (), то

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