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 <em>a</em> and common ratio |<em>r</em>| < 1. Then the <em>n</em>-th partial sum (the sum of the first <em>n</em> terms) of the sequence is
Multiply both sides by <em>r</em> :
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
Given:
12cm to 2.5mm
To find:
The simplified for of given statement.
Solution:
We know that,
1 cm = 10 mm
12 cm =120mm
We have,
12cm to 2.5mm
It can be written as
Therefore, the value of 12 cm to 2.5 mm is 48 or 48:1.
Let s equal the number of shirts she can buy
140 > $28.50 + $20.75s
111.50 > 20.75s
5.37 > s
so we round down. she can buy 5 shirts, plus the one dress and she would spend less than $140
If the time taken by 14 inches wide is one hour then the blade of 12 inches wide will take 1 hour 17 minutes to mow a lawn.
What is width?
The width of something is the measurement of one side of a body. It is generally less than length of that body or shape.
How to calculate time?
We have been given time of 1 hour if blade is 14 inches wide and we have to calculate time taken by 12 inches wide blade:
It will be as 14/12* 1 hour
=14/12
=1.167
=1.17 hour
Hence the time taken by the blade of 12 inches wide will be 1 hour and 17 minutes.
