( x+ 1/x)^6 = #160; ^6C+0(x)^6 + ^C_1 (x)^5 #160; ( 1/x) + #160;^6C_2 (x)^4 ( 1/x)^2 + #160;^6C_3 (x)^3 ( 1/x)^3 + ^6C_4 (x)^2 ( 1/x)^ ...

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Sum of n Terms

Expand x+ 1...

Question

Expand ${(x + \frac{1}{x})}^{6}$

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Solution

${(x + \frac{1}{x})}^{6}$
$=^{6} C + 0 (x)^{6} +_{1}^{C} (x)^{5} (\frac{1}{x}) +^{6} C_{2} (x)^{4} {(\frac{1}{x})}^{2} +^{6} C_{3} (x)^{3} {(\frac{1}{x})}^{3} +$
$^{6} C_{4} (x)^{2} {(\frac{1}{x})}^{4} +^{6} C_{5} (x) {(\frac{1}{x})}^{5} +^{6} C_{6} {(\frac{1}{x})}^{6}$
$= x^{6} + 6 (x)^{5} (\frac{1}{x}) + 15 (x)^{4} (\frac{1}{x^{2}}) + 20 (x)^{3} (\frac{1}{x^{3}}) + 15 (x)^{2} (\frac{1}{x^{4}}) + 6 (x) (\frac{1}{x^{5}}) + \frac{1}{x^{6}}$
$= x^{6} + 6 x^{4} + 15 x^{2} + 20 + \frac{15}{x^{2}} + \frac{6}{x^{4}} + \frac{1}{x^{6}}$

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