Now, I could also define itīy not explicitly writing the sequence like this. So this just says, all of theĪ sub k's from k equals 1, from our first term, all This right over here is the sequence a sub kįor k is going from 1 to 4, is equal to thisĪt it this way, we can look at each of these as But I want to make usĬomfortable with how we can denote sequences andĪlso how we can define them. Of different notations that seem fancy forĭenoting sequences. So we could call thisĪn infinite sequence. Pattern going on and on and on, I'll put three dots. This is infinite, to show that we keep this Keep adding the same amount, we call these Infinite sequence- let's say we start atģ, and we keep adding 4. So this one we wouldĬall a finite sequence. And let's say I only have theseįour terms right over here. Infinite number of numbers in it- where, let's say, I Have a finite sequence- that means I don't have an And all a sequence is isĪn ordered list of numbers. Video is familiarize ourselves with the notion of a sequence. I assume for quizzes however that they will continue to specify the start 1, so just work around it. You can easily avoid this problem in your own work by explicitly starting your K to start at 0. In modern Computer Science(Programming), we don't work with Indexes like this any longer, and starting an Index at 1 is generally fallen out of fashion largely in part of this constant need to work around the problem. We need to subtract 1 to bring back that balance.
The current Index can be seen as offset by 1 due to starting at 1. If We look at K=1 and did not subtract 1 from the current index we would actually get 1+3(1) = 4 or 1+3(2)=7.
This number increments each time across the "loop" and can be seen as similar to the Sigma∑ notation's looping functionality in that respect.) PreNote: ( k=1 is an index location, like finding a book in a library. This is essentially a "hack" to avoid counting your current "index" location against the math.
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