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

The modified Abel lemma on summation by parts has been applied in many ways recently to
determine closed-form evaluations for infinite series involving generalized harmonic …

A recent paper of Furdui and Vălean proves some results about sums of products of “tails” of
the series for the Riemann zeta function. We show how such results can be proved with …

We present some historical aspects to the famous Basel problem, which a number of brilliant
mathematicians attempted, and which had remained unsolved for over ninety years. It was …

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 …

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(Almost) Impossible Integrals, Sums, and Series Page 1 Problem Books in Mathematics Cornel Ioan
Vălean (Almost) Impossible Integrals, Sums, and Series With foreword by Paul J. Nahin Page 2 …

In this paper, we use Abel's summation formula to evaluate several quadratic and cubic
sums of the form F_N (A, B; x):= ∑ n= 1^ N (A-A_n)(B-B_n) x^ n, x ∈-1, 1 FN (A, B; x):=∑ n …