Answer
$1+\frac{6}{x}+\frac{15}{x^{2}}+\frac{20}{x^{3}}+\frac{15}{x^{4}}+\frac{6}{x^{5}}+\frac{1}{x^{6}}$
Work Step by Step
$(1+\frac{1}{x})^{6}=\,^6C_0\times1^{6}\times(\frac{1}{x})^{0}+\,^6C_1\times1^{5}\times(\frac{1}{x})^{1}+\,^6C_2\times1^{4}\times(\frac{1}{x})^{2}+\,^6C_3\times1^{3}\times(\frac{1}{x})^{3}+\,^6C_4\times1^{2}\times(\frac{1}{x})^{4}+\,^6C_5\times1^{1}\times(\frac{1}{x})^{5}+\,^6C_6\times1^{0}\times(\frac{1}{x})^{6}$
$=(1\times1\times1)+(6\times1\times\frac{1}{x})+(15\times1\times\frac{1}{x^{2}})+(20\times1\times\frac{1}{x^{3}})+(15\times1\times\frac{1}{x^{4}})+(6\times1\times\frac{1}{x^{5}})+(1\times1\times\frac{1}{x^{6}})$
$=1+\frac{6}{x}+\frac{15}{x^{2}}+\frac{20}{x^{3}}+\frac{15}{x^{4}}+\frac{6}{x^{5}}+\frac{1}{x^{6}}$
