All three series converge, so the answer is D.
The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.
Consider a geometric sequence with the first term a and common ratio |r| < 1. Then the n-th partial sum (the sum of the first n terms) of the sequence is

Multiply both sides by r :

Subtract the latter sum from the first, which eliminates all but the first and last terms:

Solve for :

Then as gets arbitrarily large, the term will converge to 0, leaving us with

So the given series converge to
(I) -243/(1 + 1/9) = -2187/10
(II) -1.1/(1 + 1/10) = -1
(III) 27/(1 + 1/3) = 18

8 0

3 years ago

A 20kg patient requires a 500 mg dose of a particular drug solution contains 100 mg/tsp. How many milliliters of the solution sh

Annette [7]

Answer:

The answer is "25 ml".

Step-by-step explanation:

Dose $= 500 \ mg\\\\$

Solution $= 100\ \frac{mg}{teaspoonful}\\\\$

Calculating the Conversions:

Teaspoonful $= 5 \ ml \ \text{(Ounce = 30 ml = 6 Tablespoonsful)}$

$\therefore\\\\Solution = \frac{100\ mg}{ 5\ ml} = 20\ \frac{mg}{ml}\\\\Dose \ volume = \frac{500\ mg}{ 20\ \frac{mg}{ml}} = 25\ ml$

8 0

3 years ago

What is the percent of 7/12

RoseWind [281]

First you set up the problem- 7/12=x/100. then you cross multiply 7×100=700 then divide 12 into 700 so 700÷12=58.333333333333 and so your percentage is 58.3%

5 0

4 years ago