Step-by-step explanation:
we see that from one term to the next the change is that the numerator increases by 1, the denominator increases by 1, and the sign flips.
so, numerator and denominator simply increase linearly with n, and flipping the sign is always done by putting a factor of -1 to the power of n.
if the starting point is n = 1 and f(1) = 1/6, then the explicit equation is
f(n) = (-1)^(n-1) × (n-1 + 1)/(n-1 + 6) =
= (-1)^(n-1) × n/(n+5)
but as with series themselves, the starting point can be also n = 0 and f(0) = 1/6.
and then the explicit equation is looking like
f(n) = (-1)^n × (n + 1)/(n + 6)
