Turner Chang
08/17/2024 · Junior High School
13. Explain what is wrong with this solution. \( 1+2+4+8+\ldots \) is an infinite geometric series with \( a=1 \) and \( r=2 \). \( \therefore S_{\infty}=\frac{1}{1-2}=-1 \) \( \therefore 1+2+4+8+\ldots=-1 \) So by adding infinitely many positive numbers we get a negative answer
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The error is in using the formula for the sum of an infinite geometric series with a common ratio greater than 1, which leads to an incorrect conclusion about the sum of the series.
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