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

In this paper, we evaluate in closed form several different series involving the harmonic
numbers and skew-harmonic numbers. We consider two classes of series involving these …

Infinite series involving Riemann's zeta and Dirichlet's lambda tails, and weighted by three
harmonic-like elementary symmetric functions are examined. By means of integral …

In this paper, we present a formula for generating various exotic series in the spirit of Ovidiu
Furdui and Alina Sintamarian. Our new series (evaluated in closed form) involve Bernoulli …

Let $(a_n) _ {n\geq 0} $ be an arbitrary sequence and $(a_ {\lfloor n/k\rfloor}) _ {n\geq 0} $
its dual floor sequence. We study infinite series and finite generalized binomial sums …

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 …

Since f is strictly increasing we get that f is injective. We also have that f is surjective and it
follows that f is bijective. Since f (2)= 2 we have that g′(2)= 1 f′(2)= 1 9 g^ ′ (2)= 1 f …