Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x.
-Use Gauss's function, $f ( n ) = \frac { 1 } { 2 } n ^ { 2 } + \frac { 1 } { 2 } n$, to find a natural number $n$ such that the sum of the first $n$ natural numbers is 10 .
A) 6
B) 3
C) 5
D) 4

Question

Quizplus · Accepted Answer

The sum of the first $n$ natural numbers is given by $f(n) = \frac{1}{2}n^2 + \frac{1}{2}n$. Setting this equal to 10 and solving for $n$, we get $n^2 + n - 20 = 0$. Solving this quadratic equation, we find $n = 4$.

Find All Fixed Points for the Function by Setting the Function