This is a geometric progression with first term 1 and common ratio -x. For a geometric progression to converge, its common ratio must be between -1 and 1. In this case, if x is between -1 and 1, the progression converges.
Using the formula for the sum of an infinite geometric progression, the sum of this series is:
S = 1 / (1 + x)
Therefore, if x is between -1 and 1, the sum of the infinite progression 1-x+x^2-x^3+…… is 1 / (1 + x).
What is the sum of infinity of the progression 1-x+x^2-x^3+…….
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