Summation of functions!

Algebra Level 5

The function f ( x ) f(x) is symmetric about the line x = 1 x=1 and is odd. If r = 0 [ f ( 1 + 4 r ) ] r = 8 \displaystyle \sum_{r=0}^\infty \left [ f(1+4r) \right]^r = 8 , find the value of 8 f ( 1 ) 8f(1)


The answer is 7.

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