Beautiful proofs (#1) : Divergence of the harmonic series

The harmonic series are as follows:

And it has been known since as early as 1350 that this series diverges. Oresme’s proof to it is just so beautiful.

Now replace ever term in the bracket with the lowest term that is present in it. This will give a lower bound on S1.

Clearly the lower bound of S1 diverges and therefore S1 also diverges.
But it interesting to note that of divergence is incredibly small: 10 billion terms in the series only adds up to around 23.6 !

Lawrence Joseph Bader, a cookware salesman from Ohio, disappeared in 1957 whilst on a fishing trip at Lake Eerie. Authorities found his empty boat, tackle, but Lawrence was nowhere to be seen. A freak storm made it probable that Bader had been injured and died. In 1960, he was officially declared dead. His wife, Mary Lou, was heavily pregnant with their fourth child and was understandably devastated. That was until, in 1965, Bader was miraculously found alive; Living as John ‘Fritz’ Johnson, a local TV personality, in Omaha, Nebraska.

It was only by sheer coincidence that Lawrence was recognised. On February 2, 1965, Johnson was at an archery tournament in Chicago when he was spotted by an old friend. Bader’s 21-year-old niece, Suzanne Peika, then approached him to have a look. Convinced, she asked him, “Pardon me, but aren’t you my Uncle Larry Bader, who disappeared seven years ago?” Johnson laughed it off, but Mrs. Pieka insisted that had his fingerprints compared with Bader’s military records. They matched. Johnson was now faced with the fact that all his memories were false and that he had two wives.

This case has been described as one of the most baffling amnesia disappearances on record, and it will never be properly answered as Lawrence/John had no recollection of the events leading up to it.

anonymous asked:

About jealous!Rick, picture this ... Rick and Michonne dining with some members of the Kingdom. Random Kingdom guy takes an interest in Michonne and says to Rick "I take it this one's yours?" whilst licking his lips at our Queen (creep!). Rick looks the guy up and down and drawls out "Yeah.." in that sexy ass southern accent, while placing his Colt Python on the table and tapping the barrel - starring the guy down as he says "The gun's mine too."

Ok ok… Dave Chappelle, Bill Murray and Norman Reedus walk in to a bar right.. door gets locked behind them and the 5 people inside gets to stay and hangout for the whole night… there is no punch line it’s just an excerpt from our life last night. (The selfie is actually Daves idea and Norman is probably the nicest guy ever and bought our drinks and greeted us like old friends.. wtf was my life last night?) ps thankyou to the bar manager Sam at PROOF for being super cool and letting stay and hang. ||   joe_nicol  [IG]

Creepypasta #1048: I Am A Truck Driver, And There Is A Reason I Don't Stay In Motels Anymore

Length: Medium

I have been a truck driver for some time now, and I have experienced many things on the road. Some have stayed with me for years, whilst some will probably stay with me forever. One of these experiences will for sure stay with me until the day I die.

I had been placed on a very long journey, taking a load 10 hours cross-country. There was nothing but dreadful music on the radio and I was beginning to get tired. It had gotten dark some time ago and was now extremely late. I decided to call in for the night at the next motel I came across. I didn’t even care if it was a bad one.

I now really wish I had.

I pulled up and looked around. The place looked awful. The paint was peeling off the walls, the windows were dirty, and there were multiple letters missing from the sign. The strangest part was that there were no cars in the parking lot. On any other occasion I would have taken that was a strong warning to stay away, but I’d been driving all day and did not have the energy to get back in the truck and drive somewhere else.

I went over to the reception and there was no one there. I rang the bell and still no one came. I waited a few more minutes, repeatedly ringing the bell. Annoyed, I turned round and began to walk away, but then I heard a voice. I looked round to see an elderly man with very few teeth grinning at me wildly. He welcomed me to the motel and asked me if he could be of assistance. 

I told him that I needed a room for the night and that I’d like a room with a view of my truck. I always ask this at quiet motels, it makes me feel more secure for some reason. 

He fumbled around for a bit and then threw me a key with a room number on it. I paid him upfront because I’d be setting off early in the morning. As I was walking up the stairs, I heard him say in a muffled tone “You have a great night sleep”. He then chuckled to himself quietly. This should have crept me out, but I was far too exhausted to care.

The first thing I noticed when I entered my room was that it was not facing my truck, like I’d asked. Instead it was facing the dumpsters on the other side of the building. The bed was comfy and the room was big, but I couldn’t help but feel that something wasn’t right. There were stains on the carpet - dark stains. The walls were covered in marks, and there was something in a plastic bin bag in the bath. I couldn’t tell what it was but it was big, I lifted the top to see in and I was almost sick. Inside was the head of a pig, not nicely severed like a butcher would do, but a deep, rough cut. This was absolutely disgusting, but as the walls were crawling with cockroaches anyway, I decided it best not to use the shower or the bath and drew the curtain across. I tried to forget about what I had seen.

I awoke not to the sound of my alarm clock, but the sound of voices outside my room. It was two in the morning - who would be out of bed at that time? I assumed it to be another guest and tried to get back to sleep. But before I could, I heard the unmistakable sound of a key in the lock. 

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