The given geometric series as shown in the question is seen to; Be converging with its' sum as 81
<h3>How to identify a converging or diverging series?</h3>
We are given the geometric series;
27 + 18 + 12 + 8 + ...
Now, we see that;
First term; a₀ = 27
Second Term; a₁ = 2(27/3)
Third term; a₂ = 2²(27/3²)
Fourth term; a₃ = 2³(27/3³)
Thus, the formula is;
2ⁿ(27/3ⁿ)
Applying limits at infinity gives;
2^(∞) * (27/3^(∞)) = 0
Since the terms of the series tend to zero, we can affirm that the series converges.
The sum of an infinite converging series is:
S_n = a/(1 - r)
S_n = 27/(1 - (2/3)
S_n = 81
Read more about converging or diverging series at; brainly.com/question/15415793
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Answer:
Simplify and solve and get x=-5
Step-by-step explanation:
2/3x - 1/2= 1/3 + 5/6x
2/3x - 5/6x= 1/3 + 1/2
-1/6x= 5/6
x=-5
Let's the name the first number x and the consecutive number x + 1. The sum of both of these numbers equals to 53.
We now have our equation:
x + x + 1 = 53
Now solve for x.
x + x + 1 = 53
2x + 1 = 53 <-- Combine like terms
2x = 52 <-- Subtract 1 from each side
x = 26
So, the first number is 26 and the second number is 27.
His tip was a total of $6.26
