Does the celebrated harmonic series diverge or converge? Discover a proof using the integral test. Then generalize to define an entire class of series called p-series, and prove a theorem showing when they converge. Close with the sum of the harmonic series, the fascinating Euler-Mascheroni constant, which is not known to be rational or irrational.

Logic is intellectual self-defense against such assaults on reason and also a method of quality control for checking the validity of your own views. But beyond these very practical benefits, informal logic-the kind we apply in daily life-is the gateway to an elegant and fascinating branch of philosophy known as formal logic, which is philosophy's equivalent to calculus. Formal logic is a breathtakingly versatile tool. Much like a Swiss army knife...

In the Kenyan bush, a small-time ivory dealer fights to stay on top while forces mobilize to destroy his trade. When he turns to his younger cousin, a conflicted wildlife ranger who hasn't been paid in months, they both see a possible lifeline. The plummeting elephant population in Africa has captured the attention of the world, and as the government cracks down, both poachers and rangers face their own existential crises-what is the value of elephant...

Freda Kelly was just a shy Liverpudlian teenager when she was asked to work for a local band hoping to make it big. Though she had no concept of how far they would go, Freda had faith in The Beatles from the beginning and The Beatles had faith in her. Many people came in and out of the band's circle as they grew to international stardom, but Freda remained a staple because of her unfaltering loyalty and dedication. As The Beatles' devoted secretary...

A nameplate about to be put on a statue of Admiral Hornblast goes missing and Huckle, Sally and Lowly try to uncover what happened to it. // Pig Will and Pig Won't are playing spies. However Pig Won't suddenly finds himself out of the game when his Secret Spy Ring disappears!

Nico Robin lends her many hands to an overmatched gang of revolutionaries in a frigid land of eternal suffering, and Usopp bulks up to avoid becoming a snack for a hungry, hungry island!

The earliest Christians were in fact Jews - essentially, a Jewish sect of Jesus followers. They followed Jesus and respected his teachings as if he were much like a modern-day rabbi. And they adhered to the laws of Moses - which means they circumcised, ate Kosher, and respected Saturday as the Sabbath. So why is there such a separation between Judaism and Christianity today?

Gangster Eddie Kagel finds himself in Hell to do the Devil's bidding in this noir classic that centers around revenge, love, and doing the right thing. After an agreement between Eddie and the Devil, Eddie returns to Earth to ruin the life of a judge and to seek revenge on the trusted lieutenant who sent him to his fiery demise. Little goes right for the duo as Eddie continuously enhances the reputation of the judge and, somehow, finds love.

In Tunisia, young women and men working the harvest develop new feelings, flirt, try to understand each other, find - and flee - deeper connections.

An Elf is left behind by Santa to help rescue the Harper family from a lousy Christmas. The Elf and the family get more than they bargained for, as the kids help the Elf discover his special powers and true identity as a budding superhero.