Question

write the following using sigma notation and then evaluate. the sum of the terms 2k for k=2,3,…5. provide your answer below:

Answer 1

We can express the sum of the terms 2k for k=2,3,…5 using sigma notation and evaluate it to find the answer. The sum is 28.

Step-by-step explanation:

The given expression is the sum of the terms 2k for k=2,3,…5. To express it using sigma notation, we can write it as Σ(2k) from k=2 to 5. This means that we need to sum up all the values of 2k when k takes on the values 2, 3, 4, and 5.

Using the sigma notation, we can write it as Σ(2k) for k=2,3,4,5. Expanding this notation, we have 2(2) + 2(3) + 2(4) + 2(5).

Calculating the sum, we get 4 + 6 + 8 + 10 = 28. Therefore, the sum of the terms 2k for k=2,3,…5 is 28.

Answer 2

To express the sum of the terms 2k using sigma notation, we can write it as follows:

∑(2k)

The sigma notation represents the sum of terms, where the variable k takes on values starting from 2 and increasing by 1 until it reaches 5.

Now, let's evaluate this sum:

∑(2k) for k = 2, 3, …, 5

= (2 * 2) + (2 * 3) + (2 * 4) + (2 * 5)

= 4 + 6 + 8 + 10

= 28

Therefore, the sum of the terms 2k for k = 2, 3, …, 5 is 28.