Power dissipation in resistor from triangle wave
The full band formula:
P = (U^2)/3R  (U means the peak voltage of the triangle wave)

This is practically the same as if limited to 5th harmonic because the 7th or higher ones are so weak. The error is about 1,5%

The bandlimited version needs a fourier series expansion. The peak amplitude of Nth harmonic (N=1,3,5,7,....) is 8*U/(pi*N)^2 . The power of the Nth harmonic is (8*U/(pi*N)^2)^2/2R. Calculate this for N=1,3,and 5. Add the powers. You will end to 98.6% of the full band power.