+49 ]Find the sum of all values of n that satisfy 1/n-1 + 1/n+1 = 3/n
help is appreciated.
+14995 Find the sum of all values of n that satisfy 1/n-1 + 1/n+1 = 3/n
help is appreciated.
Hello Guest!
\(\color{BrickRed}1/n-1 + 1/n+1 = 3/n\\ \frac{2}{n}=\frac{3}{n}\\ n⇒\pm\infty \)
The function has no zero.
Because point calculation comes before line calculation,
you have to put the divisors in brackets.
\(1/(n-1) + 1/(n+1) = 3/n\)
\(\frac{1}{n-1}+\frac{1}{n+1}=\frac{3}{n}\\ \frac{n^2+n+n^2-n}{n(n^2-1)}=\frac{3(n^2-1)}{n(n^2-1)}\\ 2n^2=3n^2-3\\ n^2=3\\ n=\pm \sqrt{3}\)
\(n\in\{-\sqrt{3},\sqrt{3}\}\)
!
