Topic: natural numbers (sigma notation)

[slim trail]

the basic idea to series reindexing is this

[
\sum_{k= i}^n a_n = \sum_{k=i \pm c}^{n \pm c} a_{n\mp c}
]

[slim trail]

if you add to the bounds, you subtract whats in the series

if you subtract in the bounds, you add whats in the series

does this make sense?

[stone estuary]

wait what does this symbol mean?

in the middle

[slim trail]

its the same as $\pm$ but im denoting it this way to show how you subtract when you add in the bounds

[stone estuary]

plus or minus?

[slim trail]

like uh

i will write it better

[
\sum_{k= i}^n a_k = \sum_{k=i + c}^{n + c} a_{k - c} \
\sum_{k= i}^n a_k = \sum_{k=i - c}^{n - c} a_{k + c}
]

there you go

[stone estuary]

yess

[slim trail]

so like

here they did 0 - 1 to the bounds of the first series

so you need to add 1 to a_n (a^n b^(3-n) here)

does this make sense

[stone estuary]

wait give me some minutes haha

to think about it

[slim trail]

no worries lmao

[stone estuary]

wait do I have to know exactly what n is?

noo I meant a and b

[slim trail]

wdym

oh

no

you dont

[stone estuary]

ok

[slim trail]

you just have to use this

[stone estuary]

aaa okk

wait

if you have time

could you show me a similar example of what you mean

step by step

@slim trail

[slim trail]

uh sure lemme find something

[stone estuary]

thank youuu

[slim trail]

like

take the series

[
\sum_{i=2}^{n-1} i^2
]

[slim trail]

we can reindex this by saying

[
\sum_{i=2 \c g{+1}}^{n-1\c g{+1}} (i\c b{-1})^2
]

[slim trail]

so it becomes [
\sum_{i=3}^{n} (i-1)^2
]

[stone estuary]

aaa ye like you did here

[slim trail]

yeah

[stone estuary]

was that all?

[slim trail]

yep

[stone estuary]

thank youu

[slim trail]

i can give another example if you wish

[stone estuary]

but I have one more question

[slim trail]

yeah

[stone estuary]

what is the point of reindex?

[slim trail]

to make things look nicer LOL

[stone estuary]

yesss tysm

[slim trail]

sometimes it makes what you are looking for more uh, apparent?

[stone estuary]

aaa hahah the English maths vocabulary make me confused 😭

[stone estuary]

yeyee

understood

[stone estuary]

but yes I would like that

[slim trail]

pff understandable

[slim trail]

mm i just dont know what more to add? 😭

[slim trail]

like i think it is just really this concept

[stone estuary]

ahaha hmm

[stone estuary]

okok

maybe I can try to finish the task I needed help with?

and if not I can ask again

[slim trail]

okii

[stone estuary]

like if I can’t solve it

[stone estuary]

yess but thanks

[slim trail]

i have to go now sadly i got like a presentation to do 😅

you can open a new help channel if you are still stuck

[stone estuary]

but do you want me to use the reindex for both of the sums

[slim trail]

but i will say even after you reindex you need to do some manipulations to get what they are showing

[stone estuary]

aaa no problem! Good luck with the presentation

[stone estuary]

yess understood

[slim trail]

no the first one, like subtract -1 because they go from like

0 to -1

and 4 to 3

[slim trail]

thank you! :D

[stone estuary]

aaaaaa yesss understood!!

I will try now haha

[slim trail]

okiii!

i think its better if you close this and then reopen if u get stuck

you can type

what was it

.solved?

[stone estuary]

yeye okei

[slim trail]

just for new helpers to not have to reread everything

[stone estuary]

okk

so I can just write solved now?

and open a new if I need more help?

[slim trail]

yess

exactly

[stone estuary]

okk tyyy

[slim trail]

goodluckk you got this

[stone estuary]

.solved