f[x_] = x - 0.8 - 0.2 (sinx)
x0 = Pi;
n = 20;
NewtonsMethodList[f, {x_, Pi}, 20] :=
NestList[# - Function[x, f][#]/Derivative[1][Function[x, f]][#] &, Pi, 20]
I want to apply the newton raphson method to $x - 0.8 -0.2 \sin x$ and have little experience with Mathematica, but am told this is an efficient and useful tool to find a root. Based on the information in MathWorld, I tried this out, and a number of combinations, but do not understand how to get the series of values I would expect.
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