2.2.1 Summing it up with Sigma
Name:
2-31. Use the definition of summation notation above to write out the following sums in expanded form. Then calculate
each sum's value. Note: The first one has been expanded for you. The second one has been partially expanded.
a)
b)
c)
d)
e)
f) For part (b) above, identify the argument __________________________ and the index ___________________.
2-32. Waylon wrote the following expansion for the sum below. Explain what Waylon did incorrectly in his expansion.
Sums that do not increment by one, such as the one Waylon tried in problem 2-32, are going to be important later in the
chapter. The next few problems will develop a method for writing sigma notation to add up sums like these that do not
change by one unit each time.
2-34. Find a rule for a linear function f such that f(1) = 2.2 and f(5) = 3. Write the function in slope-intercept form. Hint:
Write the coordinates of two points through which the line will go.
2-35. Use the result of the previous problem to express 2.2 + 2.4 + 2.6 + 2.8 + 3 in sigma notation. (Do not find the sum.)
Hint: Change the x to a different letter for the index.
2-36. Use the following sum to answer the questions below.
3.6 + 4.0 + 4.4 + 4.8 + 5.2
a) Use sigma notation to express the sum.
b) What changes would you make in the notations for the sum
4.0 + 4.4 + 4.8 + 5.2 + 5.6 ?
2-37. Suppose that we wish to express 3.6 + 4.0 + 4.4 + 4.8 + … + 23.2 in sigma notation where the index begins at 0.
a) Explain why the function to be summed is 0.4k + 3.6 .
b) What is the maximum value of k ?
c) Express the sum in part (a) using sigma notation.
d) Use the same idea to express 2.5 + 2.7 + 2.9 + 3.1 + … + 22.5 in sigma notation where the index k begins at 0.
Additional Practice: Calculate each sum.
8
 5k  2
k 4
5
 5(2
k
)
k 2
Write each sum using sigma notation where the index k begins at 0.
18 + 23 + 28 + 33 + 38 + 43 + 48
1.4 + 1.8 + 2.2 + 2.6 + 3