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Let \(s=\sigma+it\in C\) and \(\sigma>1\). Define \(\zeta(s)=\sum_{n=1}^\infty\frac{1}{n^{s}}\).

Evaluate \(\lim_{s \rightarrow 1}(1-s) \frac{\zeta'(s)}{\zeta(s)}\).

Find the product of the three, smallest, non-integral, positive solutions of the equation

\(\lfloor a\rfloor\lceil a\rceil=a^2\)

Given initial value for F1 = 0 and F2 = 1.We know that F3 = F2+F1 (the next term is the sum of the two preceding terms). What is the most ...

Suppose f is a function such that \( f:\mathbb{Z} ^+\to \mathbb{Z} ^+ \) satisfying

\(f(1)=1, f(2n)=f(n)\) and \(f(2n+1)=f(2n)+1\),

for all ...

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