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# C1- Sequences - sum of question type?

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Attachment 532481532483
You can't use the formula and its too much to work out without any sort of technique
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2. The first thing you should know is that its a series
3. Its the sum of the series from 1 to 100 so x1+ x2+ x3 + ... + x100 and just use the formula in the formula book to work it out
4. (Original post by SalazarSlytherin)
Its the sum of the series from 1 to 100 so x1+ x2+ x3 + ... + x100 and just use the formula in the formula book to work it out
Isn't it the formula for arithmetic series only? If the difference is the same?
5. (Original post by Questioness)
Attachment 532481532483
You can't use the formula and its too much to work out without any sort of technique
Write out the values of and see if you notice some sort of pattern...
6. (Original post by Questioness)
Attachment 532481532483
You can't use the formula and its too much to work out without any sort of technique
Write out the first four or so terms. You should see a simple pattern.
7. (Original post by SalazarSlytherin)
Its the sum of the series from 1 to 100 so x1+ x2+ x3 + ... + x100 and just use the formula in the formula book to work it out
(Original post by XOR_)
a = 1 = x1, find d (common difference) and use sn=(n/2)(2a+(n-1)d)
It's not an arithmetic series. (as can be seen multiple times throughout the question).
8. (Original post by Zacken)
It's not an arithmetic series. (as can be seen multiple times throughout the question).
So it is either equal to -1/2 or 1. How exactly do I work it out?
9. (1*50) + (1/2 * 50) = 75
10. (Original post by Questioness)
So it is either equal to -1/2 or 1. How exactly do I work it out?
Are you sure it's -1/2? If so, just replace my thing below with (1+1+ + ... ) -(1/2 + 1/2+ 1/2 + ... + 1/2) instead

Anyways, if you're adding up 1 + 1/2 + 1 + 1/2 + ... 100 times, you can just split it into (1+1+1+...+1) + (1/2 + 1/2+1/2+1/2) 50 times each.

Adding the same thing up a number of times has a name, it's called multiplication. So 1 + 1 + 1 + ... + 1 50 times is 1 * 50.

(just check whether it's -1/2 or +1/2)
11. (Original post by Questioness)
So it is either equal to -1/2 or 1. How exactly do I work it out?
It's equal to some 1s added together plus some -1/2s added together. How many of each do you have?
12. You found out that k is 3/2.

So if you look at the first 4 terms, you can clearly see a pattern of 1, -1/2, 1, -1/2 and so on.

You need the sum of the first 100 terms. Which means, a half of those will be 1s, and the other half will be -1/2s. Thus, 50*1+50*(-1/2)=50-25=25.
13. (Original post by morgan8002)
It's equal to some 1s added together plus some -1/2s added together. How many of each do you have?
(Original post by pecora)
You found out that k is 3/2.

So if you look at the first 4 terms, you can clearly see a pattern of 1, -1/2, 1, -1/2 and so on.

You need the sum of the first 100 terms. Which means, a half of those will be 1s, and the other half will be -1/2s. Thus, 50*1+50*(-1/2)=50-25=25.
(Original post by Zacken)
Are you sure it's -1/2? If so, just replace my thing below with (1+1+ + ... ) -(1/2 + 1/2+ 1/2 + ... + 1/2) instead

Anyways, if you're adding up 1 + 1/2 + 1 + 1/2 + ... 100 times, you can just split it into (1+1+1+...+1) + (1/2 + 1/2+1/2+1/2) 50 times each.

Adding the same thing up a number of times has a name, it's called multiplication. So 1 + 1 + 1 + ... + 1 50 times is 1 * 50.

(just check whether it's -1/2 or +1/2)
Thanks!! . I understand now.

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