Sigma notation Evaluate the following expressions. ...

Question

Sigma notation Evaluate the following expressions.

(b) 10

∑ (2κ + 1)

κ=1

Accepted Answer

Welcome back, everyone. Find the value of sigma from K equals 1 up to 8 of 4K minus 3, A 96, B 102, C 120, D 136. So first of all, let's rewrite our sum sigma from K equals 1 up to 8 of 4K minus 3. What we can do is simply apply the properties of sums. We can split this expression into a sum from K equals 1. Up to 8 of 4k minus sum from K equals 1 up to 8 of 3. And now we can also rewrite it as 4 multiplied by the sum from K equals 1 up to 8 of K. we're factoring out the constant. Minus Some from K equals 1 up to 8 of 3. And now let's go ahead and apply some formulas that will allow us to identify each sum. Starting with the sum from K equals 1 up to 8 of k, we have to understand that we're adding the 1st 8 integers, 1 + 2 + 3, and so on up to 8. So the formula that allows us to do so will be identified using the formula of sigma from K equals 1 up to N of K. The formula is N multiplied by N + 1 divided by 2, right? Therefore, we can show that the sum from K equals 1 up to 8. Of K is equal to 8 multiplied by 8 + 1. Divided by 2. And that's 4 multiplied by 9, which is 36. So we can label our first sum. S 36. And now we want to identify the sum from K equals 1 up to 8 of 3. What we can do is simply remember that. Some from K equals 1 up to n. Of C where C is a constant is equal to c multiplied by n. In this case, our C is 3 and our N is 8, right? So, the sum from K equals 1 up to 8 of 3 is going to be equal to 3 multiplied by 8, which is 24. So we can label our next sum. It is equal to 24. And then we can substitute the values, right? We get 4 multiplied by 36 minus 24, and that's 144 minus 24, which is 120, meaning the correct answer to this problem is C. Thank you for watching.

Sigma notation Evaluate the following expressions. (b) 10 ∑ (2κ + 1) κ=1

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Sigma notation Evaluate the following expressions.
(b) 10
∑ (2κ + 1)
κ=1