How can...

Maybe a stupid question, but I'm struggling to follow a step in lecture notes. How is this step achieved?

\frac{1}{k}cos(k\pi)=(-1)^k

I know that in radians

cos(\pi)=-1

, but can't see how to finish it off...

The 1/k is wrong.

That's because it's not true. Try setting

k = 2

, and you obtain the remarkable equality

\frac{1}{2} = 1

.

However,

\cos(k\pi) = (-1)^k

is true. Look at the periodicity of the cos graph, and it's obvious. (If you want a rigorous proof, I suppose you could use induction.)

Sun Tower

Maybe a stupid question, but I'm struggling to follow a step in lecture notes. How is this step achieved?

\frac{1}{k}cos(k\pi)=(-1)^k

I know that in radians

cos(\pi)=-1

, but can't see how to finish it off...

You'll have to give more information than that. As it stands it looks wrong.

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