Learn how to find explicit formulas for arithmetic sequences. For example, find an explicit formula for 3, 5, 7,...

In words, the formula says to take a small step in the direction of the negative gradient. Gradient descent can't tell whether a minimum it has found is local or global.

Let's find a recursive formula for the sequence. Recall that the recursive formula gives us two pieces of information:

Oops. Something went wrong. Please try again. Uh oh, it looks like we ran into an error. You need to refresh. If this problem persists, tell us.

We wrote this program to show an interesting use case for iterating by value. You can trace how the iteration works without needing to understand the details of the formula. However, if you're …

Each individual iteration of the loop in indexOfMinimum takes constant time. The number of iterations of this loop is n in the first call, then n 1 , then n 2 , and so on.

Binary search (at least the way we saw earlier in this tutorial) uses a technique called iteration; this just means that it keeps doing the same thing again and again until it solves the problem.

c * (n-1+1) ( (n-1)/2) = cn^2/2 - cn/2 Can someone explain to me how the formula is derived? For example: why (n-1+1) and why divide by 2?

Another way to derive this formula is to let S = Sum from k to n of i, write this sum in two ways, add the equations, and finally divide both sides by 2. We have S = k + (k+1) + ... + (n-1) + n S …

It's not working because your solution is an iterative solution, not a recursive solution. A recursive solution would involve the function calling itself (Hint: your recursive case should fit on one …