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A general form of Parseval's Theorem says that if two functions are expanded in a Fourier Series
f(x) =1/2 ao + Sigma [(an cos(nx)) + bn sin(nx)]
g(x) 1/2 ao' + Sigma [(an' cos(nx)) + bn' (sin(nx)]
Then the average value, < f(x)g(x)>, is:
1/4 ao = sigma[an an' + bn bn'] prove this and using any two functions
The equivalent impedance Z of two impedances Z1 and Z2 in parallel is given by the formula 1/Z = 1/Z1 + 1/Z2.
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The group of even permutations of n symbols is denoted by A_n and is called the alternating group of degree n. Show that A_8 contains an element of order 15.
Probability - poker fullhouse. A game of poker is played with an ordinary deck of 52 cards, and each player is dealt a hand of 5 cards chosen at random
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