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Find the sum of the series 1+2^(2)x+3^(2...

Find the sum of the series `1+2^(2)x+3^(2)x^(2)+4^(2)x^(3)+"...."" upto "infty|x|lt1`.

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To find the sum of the series \( S = 1 + 2^2 x + 3^2 x^2 + 4^2 x^3 + \ldots \) for \( |x| < 1 \), we can follow these steps: ### Step 1: Define the Series Let \( S = 1 + 2^2 x + 3^2 x^2 + 4^2 x^3 + \ldots \) ### Step 2: Multiply the Series by \( x \) Now, multiply the entire series \( S \) by \( x \): \[ ...
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