Chapter 4.7, Problem 54E

a.

To determine

To computevalues for each expression.

Answer to Problem 54E

Value of ‘n’	$n\times {10}^{n+1}$	$\left(n+1\right)\times {10}^n$
1	100	20
2	2,000	300
3	30,000	4,000
4	400,000	50,000

Explanation of Solution

Given information: $n\times {10}^{n+1}$ and $\left(n+1\right)\times {10}^n$

Formula used:Replacing the figures of ‘n’ in the expression.

Calculation:

Value of ‘n’	$n\times {10}^{n+1}$	$\left(n+1\right)\times {10}^n$
1	$1\times {10}^{1+1}=100$	$\left(1+1\right)\times {10}^1=20$
2	$2\times {10}^{2+1}=2,000$	$\left(2+1\right)\times {10}^2=300$
3	$3\times {10}^{3+1}=30,000$	$\left(3+1\right)\times {10}^3=4,000$
4	$4\times {10}^{4+1}=400,000$	$\left(4+1\right)\times {10}^4=50,000$

b.

To determine

To provevalue of $n\times {10}^{n+1}$ is always, sometimes or never greater than $\left(n+1\right)\times {10}^n$ .

Answer to Problem 54E

  $n\times {10}^{n+1}$ is always greater than $\left(n+1\right)\times {10}^n$

Explanation of Solution

Given information: $n\times {10}^{n+1}$ and $\left(n+1\right)\times {10}^n$

Formula used:Using various values to check the sanity.

Calculation:As seen in the table of sub-part a., value of $n\times {10}^{n+1}$ is always greater than $\left(n+1\right)*{10}^n$ . This holds true for values that are nonzero. Had the value of ‘n’ been zero, both the terms would be equal to zero.