Let P(x) be a polynomial whose degree is 6. If P(n) =1/n for n = 1, 2, 3, 4, 5, 6, 7, compute the value P(8).
This is DEFINITELY tedious to solve!!!
The form is
P(x) = ax^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx + g
Using a computer algebra system, we have that
a =1/ 5040
b = -1/ 180
c = 23/ 360
d = -7/18
e = 967/720
f = -469/180
g = 363/140
P(x) = x^6/5040 - x^5/180 +23x^4/360 -7x^3/18+967x^2/720-469/180x +363/140
P(8) = 1/4