2:38 So you said that #2 are approaching 200, so those formula could approaching either some number or infinity, or in other words they have... _limits_ ?
This is part of the foundational concepts, of infinite sequences and series, which is a topic you typically learn in Calc 2, after exhausting all the elementary methods of integration. The entire reason this chapter exists in a Calculus book, is for concepts like Taylor series and Fourier series, which are methods to solve non-elementary calculus problems, with a numeric method. Taylor series, because they reduce a function into an infinite series of polynomial terms, that allow you to apply the power rule, and Fourier series, because they are a sum of sine and cosine functions, that allows you to take advantage of their cyclic behavior among calculus operations, for solving differential equations.
Well, I imagine that, like FC temperature conversion equations, you'd have to invert the elements of the given formula. For example: If you multiplied a(sub1) by a certain constant, then subtracted another constant to arrive at a(sub2); in order to find the value of a(sub0), you'd have to add that 2nd constant to a(sub1), then divide that number by the first constant, and VOILA! 🎉
How to write a formula of a sequence? (arithmetic, geometric, quadratic, repeating, & factorial)
th-cam.com/video/QHEDDw2790Q/w-d-xo.html
The link isn't working.
Link doesn't work
Fixed. Thanks.
Square root of 2 for problem 4?
Yes!
@@bprpcalculusbasics yeah! I win! 😄 😄
2:38 So you said that #2 are approaching 200, so those formula could approaching either some number or infinity, or in other words they have... _limits_ ?
Yes, some recursive formulas also have limits.
(1) a(n) = 3^(n-1)+1
1.4142 is the square root of 2.
No, it is *not.* It is an approximation to it.
May I ask why is this in the calculus basics channel, but not in the math basics channel? Where is the calculus part?
This is part of the foundational concepts, of infinite sequences and series, which is a topic you typically learn in Calc 2, after exhausting all the elementary methods of integration. The entire reason this chapter exists in a Calculus book, is for concepts like Taylor series and Fourier series, which are methods to solve non-elementary calculus problems, with a numeric method. Taylor series, because they reduce a function into an infinite series of polynomial terms, that allow you to apply the power rule, and Fourier series, because they are a sum of sine and cosine functions, that allows you to take advantage of their cyclic behavior among calculus operations, for solving differential equations.
It’s easier for calc students to find the videos when they study sequence and series.
The square root of 2 for problem 4
Correct!
2:30 should be 195.3125 haha I worked out my answers😂
Strange how #4 approaches root 2
It’s not strangle. I used the newton’s method with f=x^2-2 to come up with that recursive sequence
😃
@@bprpcalculusbasics It's a neat sequence
How exiting ?
*exciting
Did anyone else keep pausing to work out a₀?
4/3rds ?
Tried it but it might break patterns?
Well, I imagine that, like FC temperature conversion equations, you'd have to invert the elements of the given formula. For example: If you multiplied a(sub1) by a certain constant, then subtracted another constant to arrive at a(sub2); in order to find the value of a(sub0), you'd have to add that 2nd constant to a(sub1), then divide that number by the first constant, and VOILA!
🎉