Consider the series(adsbygoogle = window.adsbygoogle || []).push({});

1+ Σ((1/(2^k))coskx + (1/(2^k))sinkx)

(a) Show that series converges for each x in R.

(b) Call the sum of the series f(x) and show that f is continuous on R = real numbers

My thoughts:

From trig => cos + sin = 1. So, is it something like

|coskx + sinkx| / |2^k| < or = (in particular = ) 1/2^k = M. Then since ΣM = Σ(1/2^k) converges (since 1/2^n approaches 0, even though it never attains it) Thus the given series converges uniformly and therefore converges. Adding 1 will not change the fact that it converges.

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# Real Analysis : Series

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