How does a recursive formula work? Calculus 2

Learn how to work with recursive formulas. Given its recursive formula, we will list out 5 more terms of the sequence.
Worksheet here: / calculus-basics-102348401
Watch the next video to learn how to write an explicit formula for a sequence: • How to write a formula...
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[@bprpcalculusbasics]

How to write a formula of a sequence? (arithmetic, geometric, quadratic, repeating, & factorial)
ua-cam.com/video/QHEDDw2790Q/v-deo.html

[@carultch]

The link isn't working.

[@Viki13]

Link doesn't work

[@bprpcalculusbasics]

Fixed. Thanks.

[@bugsfudd8295]

Square root of 2 for problem 4?

[@bprpcalculusbasics]

Yes!

[@bugsfudd8295]

@@bprpcalculusbasics yeah! I win! 😄 😄

[@SuryaBudimansyah]

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_ ?

[@bprpcalculusbasics]

Yes, some recursive formulas also have limits.

[@fifiwoof1969]

(1) a(n) = 3^(n-1)+1

[@cyrusyeung8096]

May I ask why is this in the calculus basics channel, but not in the math basics channel? Where is the calculus part?

[@carultch]

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.

[@bprpcalculusbasics]

It’s easier for calc students to find the videos when they study sequence and series.

[@brandonschaeffer1199]

1.4142 is the square root of 2.

[@forcelifeforce]

No, it is *not.* It is an approximation to it.

[@aaronrhena7515]

The square root of 2 for problem 4

[@bprpcalculusbasics]

Correct!

[@ariel_haymarket]

Strange how #4 approaches root 2

[@bprpcalculusbasics]

It’s not strangle. I used the newton’s method with f=x^2-2 to come up with that recursive sequence

[@bprpcalculusbasics]

😃

[@ariel_haymarket]

@@bprpcalculusbasics It's a neat sequence

[@lvxingzhe2718]

2:30 should be 195.3125 haha I worked out my answers😂

[@flipperpluto_BG]

How exiting ?

[@forcelifeforce]

*exciting

[@joshuahillerup4290]

Did anyone else keep pausing to work out a₀?

[@derekmartin5340]

4/3rds ?

[@ariel_haymarket]

Tried it but it might break patterns?

[@shruggzdastr8-facedclown]

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!
🎉