Hi people,

I want to plot the partial sum from n=0 to n =6 with the given function f about the point a=0 (just the maclaurin series). Unfortunately, I am unable to make sense of the issue M’tica is highlighting.

Could someone give me a leg-up?

Edit:

After nth tries:

Does this output looks sensible?

=================

In your sum function, kkk should range from 000 to nn in order to include the f(0)f(0) term in your expansion. You can also directly compare what you obtain with the results of Series[f[x], {x, 0, n}] to figure out if you are doing things correctly. You may also be interested in the SeriesCoefficient function.

– MarcoB

Sep 13 ’15 at 14:25

2

Best to paste the Mathematica code to make it easy for members to answer. Your answer is fine but the derivative needs to be evaluated at x = 0. So use D[f[x], {x, k}] /. x -> 0 in your expression.

– Jack LaVigne

Sep 13 ’15 at 14:35

=================

1 Answer

1

=================

it’s such a long time ago, I learned Taylor and so on. If my memory serves me right:

s = Sum[D[f[x0], {x0, k}]/k! (x – x0)^k, {k, 0, n}];

ps = Table[s /. x0 -> 0, {n, 1, 4}] // Simplify

{3 Ï€ x, 3 Ï€ x, 3 Ï€ x – (9 Ï€^3 x^3)/2, 3 Ï€ x – (9 Ï€^3 x^3)/2}

With Mathematicas Series we get

Series[f[x], {x, 0, #}] & /@ Range[1, 4] // Normal

{3 Ï€ x, 3 Ï€ x, 3 Ï€ x – (9 Ï€^3 x^3)/2, 3 Ï€ x – (9 Ï€^3 x^3)/2}

Plot[Evaluate@ps /. x0 -> 0, {x, -1, 1}]

@belisarius Danke! Thanks.

– user31001

Sep 13 ’15 at 14:43