{"id":10711,"date":"2017-10-24T21:18:15","date_gmt":"2017-10-25T04:18:15","guid":{"rendered":"https:\/\/magoosh.com\/hs\/?p=10711"},"modified":"2018-10-24T03:57:12","modified_gmt":"2018-10-24T10:57:12","slug":"ap-calculus-bc-review-geometric-series","status":"publish","type":"post","link":"https:\/\/magoosh.com\/hs\/ap\/ap-calculus-bc-review-geometric-series\/","title":{"rendered":"AP Calculus BC Review: Geometric Series"},"content":{"rendered":"

What is a geometric series? A series is the sum of the terms of a sequence. What makes the series geometric<\/em> is that each term is a power of a constant base. For example,<\/p>\n

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Each term in this series is a power of 1\/2. Equivalently, each term is half of its predecessor. Whenever there is a constant ratio<\/em> from one term to the next, the series is called geometric<\/em>.<\/p>\n

Read on to find out more!<\/p>\n

\"Geometric
The series 1 + 1\/2 + 1\/4 + 1\/8 + 1\/16 + …. has a finite sum. The area of the large rectangle is equal to 2, and each smaller square or rectangle fits snugly into it.<\/figcaption><\/figure>\n

Infinity and Zeno’s Paradox<\/h2>\n

Typically there are infinitely many terms to add up in a series. So it’s usually very difficult to determine whether the answer is finite, let alone what the value of the sum could be. <\/p>\n

But how can you add up infinitely many terms in the first place???<\/em><\/p>\n

This question puzzled the ancient Greek philosophers and mathematicians. In fact, the idea of infinity perplexed Zeno of Elea (c. 490 – c. 430 BC) so much that he concluded that motion must be impossible.<\/p>\n