Let's consider the scenario after each year:
After the zeroth year, the population is: 120 000(1 + 0.04)⁰
After the first year, the population is: 120 000(1 + 0.04)¹
After the second year, the population is: 120 000(1 + 0.04)²
...
Thus, we can find the general rule:
After the nth year, the population is: 120 000(1 + 0.04)ⁿ
And after the 16th year, the population is 120 000(1 + 0.04)¹⁶ = 224 758 (rounded to nearest whole number)
a. Notice that
1/(1*2) = 1/2 = 1 - 1/2
1/(2*3) = 1/6 = 1/2 - 1/3
1/(3*4) = 1/12 = 1/3 - 1/4
and so on, which suggests the n-th term of the sum can be written as
Then the sum itself is telescoping:
b. The proof is trivial:
so the formula found in (a) is correct.
Step-by-step explanation:
2 inches on the map => 2 miles in reality
So 8 inches on the map => 8 miles in reality.
The distance between the park and the school is 8 mi.
Answer:
(12 + n/3) = 2n + 1
Step-by-step explanation:
(12 + n/3) = 2n + 1
36 + n = 6n + 3
33 = 5n
n = 33/5