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The sum underset(k=1)overset(20)sum k (1...

The sum `underset(k=1)overset(20)sum k (1)/(2^(k))` is equal to

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If f(x) = (a^(x))/(a^(x) + sqrt(a)), a gt 0 prove that (i) f(x) + f(1-x) = 1 (ii) underset(k=1)overset(2n-1)sum 2f ((k)/(2n)) = 2n-1 (iii) underset(k=1)overset(2n)sum 2f((k)/(2n+1)) = 2n