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Chapter 7: Q. 27 (page 639)

Simplify the quotients in Exercises 21鈥�28 without using a calculator .

(n+1)!(n-2)!

Short Answer

Expert verified

The value is(n+1)(n)(n-1).

Step by step solution

01

Step 1. Given information.

The given expression is(n+1)!(n-2)!.

02

Step 2. Value of the limit.

We know,

n!=n(n-1)!Therefore,(n+1)!(n-2)!=(n+1)(n)(n-1)(n-2)!(n-2)!=(n+1)(n)(n-1)

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Most popular questions from this chapter

Use any convergence test from this section or the previous section to determine whether the series in Exercises 31鈥�48 converge or diverge. Explain how the series meets the hypotheses of the test you select.

鈭�k=1鈭�12k+7

Express each of the repeating decimals in Exercises 71鈥�78 as a geometric series and as the quotient of two integers reduced to lowest terms.

0.6345345...

Explain why a function a(x) has to be continuous in order for us to use the integral test to analyze a series 鈭�k=1鈭�akfor convergence.

True/False:

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: If ak鈫�0, then 鈭�k=1鈭�akconverges.

(b) True or False: If 鈭�k=1鈭�akconverges, then ak鈫�0.

(c) True or False: The improper integral 鈭�1鈭�f(x)dxconverges if and only if the series 鈭�k=1鈭�f(k)converges.

(d) True or False: The harmonic series converges.

(e) True or False: If p>1, the series 鈭�k=1鈭�k-pconverges.

(f) True or False: If f(x)鈫�0as x鈫�鈭�, then 鈭�k=1鈭�f(k) converges.

(g) True or False: If 鈭�k=1鈭�f(k)converges, then f(x)鈫�0as x鈫�鈭�.

(h) True or False: If 鈭�k=1鈭�ak=Land {Sn}is the sequence of partial sums for the series, then the sequence of remainders {L-Sn}converges to 0.

Prove Theorem 7.25. That is, show that the series 鈭�k=1鈭�akand鈭�k=M鈭�akeither both converge or both diverge. In addition, show that if 鈭�k=M鈭�akconverges to L, then鈭�k=1鈭�akconverges tolocalid="1652718360109" a1+a2+a3+....+aM-1+L.
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