@MartinTheFirst sorry had to delete it cause I just realised my real name was on it 🤦♀️🤦♀️🤦♀️ haha I hate it so muchhhh, i can understand sigma notations fine. But I can't change series of number into that form. I don't get it haha
First if you subtract one number in the line with the one that's in front of it and you get the same number wherever you do it in the series, it's arithmatic. Meaning that a2 = a1 + d
To calculate the sum of a series that follows this pattern you think like this
Sum = (a1) + (a1 + d) + (a1 + 2d)... Then backwards: Sum = (an) + (an - d) + (an - 2d)...
Add them
2sum = (a1 + an) + (a1 + an + d - d)....
Then subtract by 2 and simplify
Sum = ((a1 + an) + (a1 + an) + (a1 + an)...)÷2
We know theres n number of (a1 + an) in the series, so the sum = n(a1 + an)÷2
This is true for all arithmic series.
Now if you do this for any arithmic series:
1, 3 , 5 , 7 = 16 =
.4 .E (2k - 1) K=1
= (2 - 1) + (4 - 1) + (6 - 1) + (8 - 1)
Now this is a simple series but you can understand the concept
@SeductiveCactus also word of advice, its important that you get good at this because holy shit the next part for your and my studies is going to need that so bad 😁😀
@MartinTheFirst okay I think I'm okay with simple ones like that haha. But what about these ones that have positive numbers and negative numbers. I did get an answer that works for all of the numbers, but all I did to get it was literal hours of trying different things, so I have no proper explanation or method on how I got it. It's probably so simple 😅 idk. I'm gonna have to some heavy studying before we go further then haha.
@SeductiveCactus Well first we check if it's an arithmetic or geometric series.
Checking for a geometric series:
a2/a1 = -7/3 = q a3/a2 = -11/7 /= q for it to be geometric a2/a1 = a3/a2 but it doesn't so it must be an arithmetic series, or it's not a series at all.
Now we look for simple patterns, we can see that every other number becomes negative. This means that it's multiplied by -1 that's raised to the power of k that's odd and even every other step in the series.
If we negate this change by making all numbers even, since we know that we need to find d = difference between each step, we can now take 7 - 3 = 15 - 11 = 19 - 15 which is indeed = 4
We now know that d = 4
we know that there's 7 numbers (steps) in the function, so we start with: .7 .E(4k) = 4, 8, 12... etc k=1
this doesnt look quite right, all the numbers should be odd, and if we compare the series each step in our series should be exactly 1 less. We try again.
.7 .E(4k - 1) = 3, 7, 11.. k=1
now we're getting close. We know that we need to make the first number negative, the second number positive, so on so forth. That's why we set -1^k
@MartinTheFirst Ohhhhhhhh. Thank you so much. Explaining it really helped my understanding. I definitely need to study up more but now I think I know where to start when doing these types of questions. Just need some practice haha. I now know where to go to ask about this subject haha 😂
