How Do You Solve x+x^2+x^3+x^4... = 14 for x?

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To solve the equation x + x^2 + x^3 + x^4... = 14, one can apply the formula for an infinite geometric series, which is valid for -1 < x < 1. This formula states that the sum can be expressed as a0 / (1 - x), allowing for the transformation of the series into a solvable equation. The discussion emphasizes the importance of using this formula correctly to find the value of x. Additionally, the thread notes that a similar question has been previously addressed, leading to its closure. The focus remains on applying the geometric series formula to derive the solution.
Niaboc67
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x+x^2+x^3+x^4... = 14

Find x

Could someone please provide an explanation on how to solve this?
 
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The formula for infinite geometric series is ##\displaystyle \sum_{n=0}^\infty a_n x^n =\frac{a_0}{1-x} ##. But this is true only for ## -1 < x < 1##. Just use this on the series to get an equation in a familiar form.
 
Same question asked in another thread with the same name, so locking this thread.

@Niaboc67, please don't start multiple threads on the same topic.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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