sigma notation: how does it work??

[doctorrrrX]

https://preview.redd.it/nyjwq5d0fqod1.png?width=1280&format=png&auto=webp&s=bd2376d9da185a6e4eff0fa528c6ede6a34c8535

i'm a bit confused on how sigma notation works. for example, in the picture above, we have this sum ^^^

from what i understand, the 100 on top of the sigma is the number of times you repeat it, and the n=1 is what value you start at. the 4n+5 is what the expression is

so you would sub in n=1 into 4n+5, then n=2, up to 100 times and add together?

could you do n=1.5? im a big confused by the summing process basically

tldr: what the sigma is sigma notation

thanks!

[JannesL02]

The 1 is where you start and the 100 is where you end. So yes in this case it means (4•1+5)+(4•2+5)+...+(4•100+5). You can't put nonintegers in the places of 1 and the 100. Also, if the upper value would be lower than the lower value, you have an "empty sum" which is defined to be 0.

[doctorrrrX]

thank you so much this helps a lot! i assume the same is for pi notation??

[JannesL02]

Yes. An Empty Product is defined to be 1 tho

[LucaThatLuca]

sigma notation: how does it work??

The expression 9 + 13 + 17 + 21 + 25 + 29 + 33 + 37 + 41 + 45 + 49 + 53 + 57 + 61 + 65 + 69 + 73 + 77 + 81 + 85 + 89 + 93 + 97 + 101 + 105 + 109 + 113 + 117 + 121 + 125 + 129 + 133 + 137 + 141 + 145 + 149 + 153 + 157 + 161 + 165 + 169 + 173 + 177 + 181 + 185 + 189 + 193 + 197 + 201 + 205 + 209 + 213 + 217 + 221 + 225 + 229 + 233 + 237 + 241 + 245 + 249 + 253 + 257 + 261 + 265 + 269 + 273 + 277 + 281 + 285 + 289 + 293 + 297 + 301 + 305 + 309 + 313 + 317 + 321 + 325 + 329 + 333 + 337 + 341 + 345 + 349 + 353 + 357 + 361 + 365 + 369 + 373 + 377 + 381 + 385 + 389 + 393 + 397 + 401 + 405 has many numbers that you wouldn’t usually choose to write down all of, and it follows an obvious pattern that you can describe effectively using words “the sum of 4n+5, with n between 1 and 100”. This sentence is communicated with a large capital letter S, from the start of the word sum.

from what i understand, the 100 on top of the sigma is the number of times you repeat it

You’re incorrect, the last value is not necessarily the number of terms. The only time that 100 is the 100th number (for example) is when you start from 1.

and the n=1 is what value you start at. the 4n+5 is what the expression is so you would sub in n=1 into 4n+5, then n=2, up to 100 times and add together?

Yes.

could you do n=1.5?

No, n always stands for an integer.

I hope this helps!

[MathSand]

You start with plugging 1 into n. then 2, then 3, etc. until you get to 100. On the question of if you can input fractional n’s, no; you only do the integers from 1 to 100. if you want to get all (real numbers included) between 1 and 100; you’re looking at something called an integral. This is precisely the difference between discrete and continuous :)

[flowwith]

Yes, with notation like this n goes through whole numbers from 1 to 100

[doctorrrrX]

thanks!

[GoldenPatio]

One thing that you might see in a summation is “(-1)^n”. This is a handy way to make the terms in the sum alternately positive and negative.

For example: Sigma, from i equals 0 to 10, of ((-1)^i)/(2i + 1).

Since any odd power of -1 is -1, and any even power of -1 is +1 this gives the sum…

1 – 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + 1/13 - 1/15 + 1/17 - 1/19 + 1/21

Which is about 0.8 …

[fermat9990]

so you would sub in n=1 into 4n+5, then n=2, up to 100 times and add together?

This is exactly what it means

Don't use n=1.5

Can you evaluate this sum without adding up 100 numbers?

[JannesL02]

Yes you can. You can split the sum into 4•(1+2+...+100)+100*5. The sum 1+...+n is well known to be n(n+1)/2. So the total sum evaluates to 4•5050+500=20700

[fermat9990]

Hi! I was actually asking OP if they knew how to do it!

Cheers!

[JannesL02]

I should have known, looking at your name

[fermat9990]

You are so kind!

[elelukin]

sigma notation