Answer:
The given series converges and 
Step-by-step explanation:
Given is 108, -18, 3,...
It is an alternate series. An alternate series is convergent if:
1. The series is decreasing.
2. If the last term (n-th term) of series converges to 0.
<u>Since each next term is less than its preceding term, so it is decreasing.</u>
First term, a = 108
Second term = -18
Common ratio, r = -18/108 = -1/6
General term, aₙ = a*rⁿ = 108*(-1/6)ⁿ
<u>When n increases to infinity, the exponent term will decreases to zero, and last term (n-th term) will converge to 0 as well.</u>
Hence, the given series converges.
Now limit will be: 
Hence,
Answer:
Mrs. Etercsid
Step-by-step explanation:
One thing we can do is just multiply the averages by the percents in each class and compare from there.
To get from percentages to decimals, we can divide by 100.
For Mr. Tats:
Homework: 25 % -> 0.25
Participation: 10% -> 0.1
Test: 40% -> 0.4
Final: 0.25 -> 0.25
For Mrs. Etercsid:
Homework: 15% -> 0.15
Participation: 10% -> 0.1
Test: 60% -> 0.6
Final: 15% -> 0.15
We can then multiply the averages by the decimals for each teacher and add them up.
Mr. Tats:
0.25 * 81 + 0.1 * 57 + 0.4 * 93 + 0.25 * 87 = 84.9
Mrs. Etercsid:
0.15 * 81 + 0.1 * 57 + 0.6 * 93 + 0.15 * 87 = 86.7
You would get the higher grade with Mrs. Etercsid
3 apples weigh 1 lb.....so 1 apple would weigh 1/3 = 0.3 lbs
I believe that 21 is d 27 over 17
I believe that 22 is d because 16 divided by 3.20 is 5
sorry if I am wrong
I hope this helps you
