Step-by-step explanation:
Explanation:
The trick is to know about the basic idea of sequences and series and also knowing how i cycles.
The powers of i will result in either: i, −1, −i, or 1.
We can regroup i+i2+i3+⋯+i258+i259 into these categories.
We know that i=i5=i9 and so on. The same goes for the other powers of i.
So:
i+i2+i3+⋯+i258+i259
=(i+i5+⋯+i257)+(i2+i6+⋯+i258)+(i3+i7+⋯+i259)+(i4+i8+⋯+i256)
We know that within each of these groups, every term is the same, so we are just counting how much of these are repeating.
=65(i)+65(i2)+65(i3)+64(i4)
From here on out, it's pretty simple. You just evaluate the expression:
=65(i)+65(−1)+65(−i)+64(1)
=65i−65−65i+64
=−65+64
=−1
So,
i+i2+i3+⋯+i258+i259=-1
31.5 miles
If she runs 2.25 miles/day and she runs 14 days, you multiply 14*2.25
Its 8$ per hour or 8/1 hour because if you line it up every hour it increases by $8
Answer:
This problem has two possible solutions.
2232
7236
Step-by-step explanation:
To be divisible by 72, a number has:
To be divisible by both 8 and 9 at the same time.
It is divisible by 8 if it's last two digits are divisible by 4.
It is divisible by 9 it the sum of it's digits is a number divisible by 9.
a23b
3b must be divisible by 4. In the thirties, the numbers that are divisible by 4 are 32 and 36. So b = 2 or b = 6.
a232
2 + 3 + 2 = 7
The higest possible value of a is 9 and the lowest is 1.
Between 8 and 16, only 9 is divisible by 9. So a = 2.
a = 2, b = 2 is one of the solutions.
a236
2 + 3 + 6 = 11
The higest possible value of a is 9 and the lowest is 1.
Between 12 and 20, only 18 is divisible by 9. So we need a = 7
