In Exercises 29–42, find each indicated sum. 4Σi=1 2i^2

Question

Accepted Answer

Hello. Everyone in this video we're going to be looking at this practice problem where we want to perform the summation of I equals one to I equal six with the expression eight I squared. So from here you can see that we want to evaluate the terms from I equals one through I equals six and the expression is eight I squared. So because we're going from 1-6, those are all the terms that we need to determine and add together. So I'm going to start with I is equal to one or our first term. So when I is equal to one, the expression becomes eight times one squared. And if I simplify this I get simply eight because eight times one squared is the same as eight times one which is just eight. And I need to evaluate for all my terms up until I is equal to six in order to figure out this summation. So I'm going to continue with I is equal to two and when I is equal to two my expression becomes eight times two squared. And when I simplify this I get eight Times two times squared is equal to four. So when I is equal to two I get 32. When I is equal to three my expression becomes eight times three squared. If I simplify this it becomes eight times three squared is nine. So when I is equal to three I get 72. When I is equal to four my expression is eight times four squared. If I simplify this I get eight times four squared is 16. So when I is equal to four I get and we still have two more terms to go. So when I is equal to five my expression is eight times five squared. If I simplify this I have eight times That is equal to 200. And my final term is when I is equal to six my expression is eight times six squared. If I simplify this, I have eight times 36 Which means that when I is equal to six I get 288. And now you can see that I've evaluated for all the terms one through six. And because it's a summation, I need to remember to add all of the terms together. So I need to add when I is equal to one I got eight plus I equal to two, I got 32 And so on for all the values that we solve. So I have 8:30-72, 1, 28 And 288. And I can sort of start reducing this. So eight plus 32 is 40 72 plus one, is 200, 200 plus 2 88 is 488. And now I have 40 plus 200 plus four year 84 88. And that gives me 728. So this becomes my final answer for when I some the terms I equals one through I equal six for the expression eight I squared. And you can see that this aligns with answer choice B. Hopefully this video helped and see you next time.

In Exercises 29–42, find each indicated sum. 4Σi=1 2i^2

Key Concepts

Summation Notation

Quadratic Functions

Evaluating Sums

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