It will diverge. Consider the Nth partial sum,
= (ln1 - ln6) + (ln2 - ln7) + (ln3 - ln8) + (ln4 - ln9) + (ln5 - ln10)
+ (ln6 - ln11) + (ln7 - ln12) + ...
+ (ln(N-5) - lnN) + (ln(N-4) - ln(N+1)) + (ln(N-3) - ln(N+2)) + (ln(N-2) - ln(N+3)) + (ln(N-1) - ln(N+4))
+ (lnN - ln(N+5))
Cancellation among terms leaves us with
= ln1 + ln2 + ln3 + ln4 + ln5 - ln(N+1) - ln(N+2) - ln(N+3) - ln(N+4) - ln(N+5)
We can write this as
Then as , the argument of the logarithm is 0, so the logarithm itself approaches -infinity. Then the limit of the series is non-zero, so it must diverge.
Write the system of equation based on the problem
"A total of 345 tickets that consists of adult tickets and students ticket were sold" could be written as:
∴ a + s = 345 <em>(first equation)</em>
"<span>the number of student tickets sold was two times the number of adult tickets sold" could be written as:
</span>∴ s = 2a <em>(second equation)</em>
<span>
Solve the system of equation
Substitute 2a as s in the first equation
a + s = 345
a + (2a) = 345
3a = 345
a = 345/3
a = 115
There are 115 adult tickets sold.</span>
Answer:
∠P = 39º
∠Q=120º
∠R = 21º
Step-by-step explanation:
m∠P+m∠Q+m∠R=180º (sum of ∠s in a triangle)
2x-3+6x-6+x=180º (substitution)
9x-9=180º (algebra)
9x=189º (algebra)
x=21º (algebra) (this is ∠R)
(2x-3)=39º (algebra) (this is ∠P)
6x-6=120º (algebra) (this is ∠Q)
answers:
What is the initial conflict?
✔ Anyone placed in the arena gets either married or killed.
What is the princess's struggle?
✔ Her lover is in the arena, and she is jealous of the girl he might have to marry.
What decision is made?
✔ The reader never finds out.
What are the consequences of the choice?
✔ The princess will either let her love die or let him marry someone else.