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A convergent series is one that ends at a set value. Some only reach that value after an infinite number of terms, requiring limits and geometric visualizations to uncover the answer. In the video is the sum of reciprocals of increasing powers of 2, now yes you can just use a/(1-r) but it's much nicer to see that if you let each term represent an area, they will all piece together into a square of area 1. You could not use integration, as this is a discrete sum with countably infinite terms inst
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A convergent series is one that ends at a set value. Some only reach that value after an infinite number of terms, requiring limits and geometric visualizations to uncover the answer. In the video is the sum of reciprocals of increasing powers of 2, now yes you can just use a/(1-r) but it's much nicer to see that if you let each term represent an area, they will all piece together into a square of area 1. You could not use integration, as this is a discrete sum with countably infinite terms inst
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