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Chapter 4: Q. 28 (page 325)

Write each of the sums in Exercises 28 in sigma notation. Identify m, n, and akin each problem.

-2n-1n+0n+1n+鈰�+nn

Short Answer

Expert verified

Here,m=-2,n=nandak=kn

鈭�k=-2nkn

Step by step solution

01

Given information

The given series is-2n-1n+0n+1n+鈰�+nn.

02

Write the series in term of summation

Rewrite the given series in term of summation.

-2n-1n+0n+1n+鈰�+nn=鈭�k=-2nkn

03

Write the conclusion

The summation is鈭�k=-2nkn.

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Most popular questions from this chapter

Given a simple proof that鈭�k=0n3ak=3鈭�k=0nak

Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.

(a) True or False: The absolute area between the graph of f and the x-axis on [a, b] is equal to|鈭�abf(x)dx|.

(b) True or False: The area of the region between f(x) = x 鈭� 4 and g(x) = -x2on the interval [鈭�3, 3] is negative.

(c) True or False: The signed area between the graph of f on [a, b] is always less than or equal to the absolute area on the same interval.

(d) True or False: The area between any two graphs f and g on an interval [a, b] is given by 鈭�ab(f(x)-g(x))dx.

(e) True or False: The average value of the function f(x) = x2-3 on [2, 6] is

f(6)+f(2)2= 33+12= 17.

(f) True or False: The average value of the function f(x) = x2-3on [2, 6] is f(6)-f(2)4= 33-14= 8.

(g) True or False: The average value of f on [1, 5] is equal to the average of the average value of f on [1, 2] and the average value of f on [2, 5].

(h) True or False: The average value of f on [1, 5] is equal to the average of the average value of f on [1, 3] and the average value of f on [3, 5].

Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.

鈭�01/2鈥�11+4x2dx

Explain why it would be difficult to write the sum 13+14+15+18+111+112+113 in sigma notation.

Use integration formulas to solve each integral in Exercises 21鈥�62. You may have to use algebra, educated guess- and- check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating. (Hint for Exercise 54: tanx=sinxcosx).

鈭�x2x3+15dx.
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