QuestionQuestion
Write the following using sigma notation and then evaluate.
The sum of the terms for .
Provide your answer below:
Studdy Solution
STEP 1
What is this asking? We need to rewrite a sum using the fancy sigma notation, and then calculate what it equals! Watch out! Make sure to start and end at the correct values of !
STEP 2
1. Rewrite the sum using sigma notation.
2. Calculate the sum.
STEP 3
The general term in our sum is .
This tells us what each piece of the sum looks like.
STEP 4
We're told that goes from to , inclusive.
These are our **starting** and **ending** values.
STEP 5
Using the sigma notation, we can write the sum as: So we're adding up the expression for each value of from to .
STEP 6
Let's write out each term of the sum:
STEP 7
Let's simplify those exponents:
STEP 8
Calculating the powers of , we get:
STEP 9
Adding the numbers inside the parentheses gives us:
STEP 10
Finally, adding all the terms together, we get:
STEP 11
The sum in sigma notation is , and its value is .
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