y=kcosh(x/k) = k(e^(x/w) + e^(-x/k))(adsbygoogle = window.adsbygoogle || []).push({});

y ~ k[1 + x/k + (1/2!)(x^2/k^2) + (1/3!)(x^3/k^3)] +...+ k[1 - x/k +(1/2!)(x^2/k^2) - (1/3!)(x^3/k^3) +...]

All odd terms except 1 cancel out.

So we are left with

y = k [2+ (2/2!)(x^2/k^2) + (2/4!)(x^4/k^4) + (2/6!)(x^6/k^6) +....]

I've been staring at this for hours and I'm supposed to show that:

y= k + (1/2k)(x^2) for k>>x

What did I do wrong??? My error lies somewhere where the twos are bolded.

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# Taylor Series Expansion

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