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(1+1/n)n=2
We move all terms to the left:
(1+1/n)n-(2)=0
Domain of the equation: n)n!=0We add all the numbers together, and all the variables
n!=0/1
n!=0
n∈R
(1/n+1)n-2=0
We multiply parentheses
n^2+n-2=0
a = 1; b = 1; c = -2;
Δ = b2-4ac
Δ = 12-4·1·(-2)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{9}=3$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3}{2*1}=\frac{-4}{2} =-2 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3}{2*1}=\frac{2}{2} =1 $
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