Math Help - Summation notation

I don't know how to write the symbol sigma on here but the lower limit is 1 and the upper limit is 4 and (xi - yi)^2. I need the method on how to do it.

Originally Posted by marie7

I don't know how to write the symbol sigma on here but the lower limit is 1 and the upper limit is 4 and (xi - yi)^2. I need the method on how to do it.

First of all, we need to be clear on what the problem is. Do you mean:

?

yes that's correct sorry I don't know how to do the symbols

Originally Posted by marie7

yes that's correct sorry I don't know how to do the symbols

OK... well this is sort of an odd sum. The and aren't involved in the indexing, so we can take them out. We get



Now the sum should be very simple to solve.

Originally Posted by AlephZero

OK... well this is sort of an odd sum. The and aren't involved in the indexing, so we can take them out. We get



Now the sum should be very simple to solve.

Well the x and y have number values and I just wanted the method so I could do it myself but here are the numbers:
for x1 = 2, x2 = -3, x3 = 10 x4 = -5, x5 = -3
for y1 = -1, y2 = 3, y3 = 5, y4 = 7, y5 = -2.

i is supposed to represent for example 1 in x1, 2 in x2 etc. Its a little i.

Originally Posted by marie7

Well the x and y have number values and I just wanted the method so I could do it myself but here are the numbers:
for x1 = 2, x2 = -3, x3 = 10 x4 = -5, x5 = -3
for y1 = -1, y2 = 3, y3 = 5, y4 = 7, y5 = -2.

i is supposed to represent for example 1 in x1, 2 in x2 etc. Its a little i.

Alright, so when I asked you previously if I had typed up the problem correctly, and you said "yes," that wasn't true, evidently. And you are now providing, in addition, a hugely crucial portion of the problem that you also neglected to mention.

So now I ask you again. Think very hard. Is this the problem:

?

yeah it is.

Well, then the easiest way to do it is just expand the sum, and substitute the values:



Simply plug in the values and do the arithmetic.

I got -146 as my answer, is that correct?

No, Marie. 'fraid not.

Hint:

Spoiler:

Your answer cannot be negative because you're taking the same of "squares". Can A squared number be negative?

I plugged the numbers in like this (2 -(-1))^2 + (-3-3)^2 + (10 - 5)^2 + (-5-7)^2

Am I right?

Originally Posted by marie7

I got -146 as my answer, is that correct?

Ah, no, I'm afraid not, for at least 3 reasons. First, I have done the arithmetic myself based on the numbers you provided, and reached a different solution. Second, your answer is a negative number, and since the expression at hand involves the sum of four squares, a negative answer is impossible. Thirdly, you have provided a question involving a finite sum with 4 terms, and supplied data for 5 terms, so something is bound to be wrong with just about any answer you come up with.

yes but the upper limit is four so I only do from 1 to four not 1 to five, does that make sense?

Originally Posted by marie7

I plugged the numbers in like this (2 -(-1))^2 + (-3-3)^2 + (10 - 5)^2 + (-5-7)^2

Am I right?

You plugged 'em in right, but unfortunately arrived at the wrong answer. What did you do after that?

Look at my last post for a hint.

Originally Posted by marie7

yes but the upper limit is four so I only do from 1 to four not 1 to five, does that make sense?

Correct!