My First Problem

First, start by finding a common denominator: $\frac{x^6}{x^6}\cdot \frac{5x^{-1}+2x^{-5}}{x^{5}}-\frac{x^5}{x^5}\cdot \frac{5+x^{-4}}{x^{6}}$ This becomes: $\frac{5x^{5}+2x^{1}}{x^{11}}-\frac{5x^{5}+x^{1}}{x^{11}}$ You then simplify: $\frac{5x^{5}+2x^{1}-5x^{5}-x^{1}}{x^{11}} = \frac{x}{x^{11}}$ Get rid of like terms: $\frac{1}{x^{10}}$ You are left with: $y = \zeta(10) = \sum_{i = 1}^{\infty} \frac{1}{x^{10}} \approx 1.00099$ Rounding to the nearest whole leaves us with 1.