prove that error between approximating function and first three terms of power series expansion is less than 1/1500

Introduction: In this solution, we prove that error between approximating function and first three terms of power series expansion is less than 1/1500.Question: Power series expansion of a function is $$P\left(x\right)=\sum_{n=0}^{\infty}\frac{\left(-1\right)^n\left(x+2\right)^n}{3^n\left(n+1\right)}$$ prove that at point x =-2.5 error between approximating function…

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