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