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The sum of the coefficients of the first...

The sum of the coefficients of the first three terms in the expansion of`(x-3/(x^2))^m ,x!=0,`m being a natural number, is 559. Find the term of the expansion containing `x^3`.

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To solve the problem, we need to find the term in the expansion of \((x - \frac{3}{x^2})^m\) that contains \(x^3\), given that the sum of the coefficients of the first three terms in the expansion is 559. Let's break this down step by step. ### Step 1: Write the General Term The general term \(T_{r+1}\) in the expansion of \((x - \frac{3}{x^2})^m\) can be expressed as: \[ T_{r+1} = \binom{m}{r} x^{m-r} \left(-\frac{3}{x^2}\right)^r \] This simplifies to: ...
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