{"id":10711,"date":"2017-10-24t21:18:15","date_gmt":"2017-10-25t04:18:15","guid":{"rendered":"\/\/www.catharsisit.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":"\/\/www.catharsisit.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