Explain sigma notation?

[LuDaCriS66]

Sorry.. I just need a quick explaination of how sigma notation works.. I'm doing my finite mathematics homework and I forgot how to do sigma notation! It's something I haven't done since grade 8.. but I'm still in high school so it's nothing to really panic about

Anyway.. how does it work??

How do you write a series of numbers such as "1 + 4 + 9 + ... + 64" into sigma notation?

How do you expand something that looks like this..... a 4 on top of sigma with i=1 under it.. and (2i - 3) to the right of it

any help is appreciated.. thanks

 

[TuffGirl]

<< How do you write a series of numbers such as "1 + 4 + 9 + ... + 64" into sigma notation? >>


8 on top of sigma with i=1 underneath... then (i^2) to the right.

<< How do you expand something that looks like this..... a 4 on top of sigma with i=1 under it.. and (2i - 3) to the right of it >>

that equals (2*1-3) + (2*2-3) + (2*3-3) + (2*4-3)


Sigma just means summation... found a decent explanation here. Hope this helps.

 

[b0mbrman]

<< How do you expand something that looks like this..... a 4 on top of sigma with i=1 under it.. and (2i - 3) to the right of it >>

that equals (2*1-3) + (2*2-3) + (2*3-3) + (2*4-3) [/i] >>

[/i] >>


I'd simplify it first

Pretend the "S" is a Sigma with a i=1 under it and a 4 on top

S(2i-3)
=S2i - S3
=2Si - 4*3
=2Si - 12
=(2 + 4 + 6 + 8) - 12
=8

It seems pretty silly now, but when you get into more complicated, knowing those rules is a lifesaver

 

[LuDaCriS66]

<< 8 on top of sigma with i=1 underneath... then (i^2) to the right >>



Yeah, that's the right answer but I don't understand how you got it.. can you please go into it in detail?? Sorry... the link you provided was good but I didn't understand some of it

 

[TuffGirl]

<<

<< 8 on top of sigma with i=1 underneath... then (i^2) to the right >>



Yeah, that's the right answer but I don't understand how you got it.. can you please go into it in detail?? Sorry... the link you provided was good but I didn't understand some of it >>

Lemme know what in particular you didn't understand and I'll fill you in, ok? The diagram with the arrows and terms defined above it sums it up well. I'm afraid I can't explain very well how to get the notation without being confusing or calling it "intuitively obvious" like this Calc prof of mine used to do.


It would also help if you enabled your PMs.

 

[LuDaCriS66]

^

Also if anyone can solve this problem for me, it'd be appreciated

'Jessica lives six blocks north and four blocks west of her school. There are 200 school days and Jessica is never absent. Is it possible for her to take a different path to school every day, assuming she walks only south and east? "

I know the answer is yes.. but why?

 

[b0mbrman]

<< ^

Also if anyone can solve this problem for me, it'd be appreciated

'Jessica lives six blocks north and four blocks west of her school. There are 200 school days and Jessica is never absent. Is it possible for her to take a different path to school every day, assuming she walks only south and east? "

I know the answer is yes.. but why? >>


Easy...you need 4 moves south and 6 moves east. Think of it as the set of all 10-digit binary numbers that have 4 0's and 6 1's

 

[LuDaCriS66]

<<

<<

<< 8 on top of sigma with i=1 underneath... then (i^2) to the right >>



Yeah, that's the right answer but I don't understand how you got it.. can you please go into it in detail?? Sorry... the link you provided was good but I didn't understand some of it >>

Lemme know what in particular you didn't understand and I'll fill you in, ok? The diagram with the arrows and terms defined above it sums it up well. I'm afraid I can't explain very well how to get the notation without being confusing or calling it "intuitively obvious" like this Calc prof of mine used to do.


It would also help if you enabled your PMs. >>



Well, I didn't understand how you got from "1 + 4 + 9 + .. + 64" to 8 on top of sigma with i=1 and i^2. How did you get the 8, the i=2, and the i to the power of 2?

Oh and I enabled my Pm's

 

[b0mbrman]

<< Well, I didn't understand how you got from "1 + 4 + 9 + .. + 64" to 8 on top of sigma with i=1 and i^2. How did you get the 8, the i=2, and the i to the power of 2? >>


8 is the last number in the series or the upper limit of summation
i=1 is the arbitrarily-chosen variable picked to represent the series (you can use n, beta, even a ...but i is the one most people use). The "1" is the first number in the series or the lower limit of summation
i^2 is the function for each addend...

 

[b0mbrman]

<< Easy...you need 4 moves south and 6 moves east. Think of it as the set of all 10-digit binary numbers that have 4 0's and 6 1's >>


BTW, the answer is 210...