Alina Sîntămărian Ovidiu Furdui Page 1 Problem Books in Mathematics Alina Sîntămărian
Ovidiu Furdui Sharpening Mathematical Analysis Skills Page 2 Problem Books in …

The logarithmic integral (7) is found in [3], the harmonic series (11) and (12) are calculated
in [7], the harmonic series (8) is calculated in [8], the harmonic series (10) is calculated in [6] …

The shear unexpectedness of the result, its simplicity of form, the brilliance with which Euler
solved it, 1 together with the many different and varied proofs given since its initial solution …

We revisit the quadratic series of Au-Yeung∑ n= 1∞ H nn 2, which is quite well-known in
the mathematical literature, and we consider its alternating sum∑ n= 1∞(-1) n+ 1 H nn 2 …

The limit equals 2. Let xn= 2 n sin 1+ 2 n sin 2+⋯+ 2 n sin nn x_ n=\sqrt n 2^ n\,\sin 1+ 2^
n\,\sin 2+ ⋯+ 2^ n\,\sin n. Since 2 n sin i≤ 2 n 2^ n\,\sin i ≦ 2^ n, we get that xn≤ 2 nn x_ n …

An Artistry of Quadratic Series: Two New Proofs of Sandham–Yeung Series | SpringerLink Skip
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