can you explain the way you did the sum please
Answers
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Two physicists explain: The sum of all positive integers equals −1/12
Their viral video introduces mathematics that laymen find preposterous, but physicists find useful.
Steven T. Corneliussen
So there you are living your life, content in your grasp on how the world works: up is up, down is down, the Sun rises in the east and sets in the west. Then, out of nowhere, a bunch of mathematicians try to tell you that the sum of all positive integers, that is, 1 + 2 + 3 + 4 + 5 + 6 + . . . and so on to infinity is equal to . . . −1/12.
Well, that's clearly ridiculous, right? How can increasingly big numbers, when added together, make a small number? How can whole numbers make a fraction? How can positive numbers make a negative?
Tony Padilla and Ed Copeland, physicists at the University of Nottingham in the UK, appear in and narrate the eight-minute video. Minute by minute, what they explain requires from the viewer no mathematical grounding beyond simple addition and a smattering of the most basic algebra. But in the aggregate, what they argue goes well beyond that simplicity.
the American Physical Society’s PhysicsCentral website offers the Physics Buzz Blog posting “Correction: Does 1 + 2 + 3 + 4 + . . . = −1/12? Absolutely Not!” It begins by pointing to a graph: “Brief Summary: 1 + 2 + 3 + 4 + . . . is not equal to −1/12, but both the infinite series and the negative number are associated with each other in a way that can be seen in this graph.”
At the Times, Overbye quips, “After watching the video myself, I checked to make sure I still had my wallet and my watch.” But he also reports something that Padilla and Copeland adduce in the video. They open the textbook String Theory, by Joseph Polchinski of the University of California, Santa Barbara, and point to a page showing his use of the mathematics in question.
On the web, Padilla has posted a write-up for physicists. He begins with this explanation:
Answer:
Which sum are you talking about
Step-by-step explanation:
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