How do I express this sum in terms of n?

[flint gulch]

i = 1 to n/2

[flint gulch]

How do I express this sum in terms of n?

[spring rune]

do you still need help with this?

[flint gulch]

I do

I separated sum(n - i + 1) into sum(n) - sum(i) + sum(1)

My main problem is the sum(i)

Wolfram alpha says it's equal to (n(n+2))/8, but I'm having trouble understanding why

[spring rune]

wanna hop on call. i can help

[flint gulch]

can't rn

[keen burrow]

So you are adding n to itself n/2 times

What do you get from that

And you are adding 1 n/2 times

Those 2 sums should be easy to convert to a normal equation

[flint gulch]

n * (n/2) for the first one and n/2 for the second sum

But I'm still confused for the sum of i

[keen burrow]

Ok but that alright since you be gotten 3 sums down to 1

Now we are just looking at the sum of 1 + 2 + 3 … n/2

There’s a famous formula for this

But you might not know it

@flint gulch

If you don’t know it I can teach it to you

Just ping me if you want to learn

[flint gulch]

@keen burrow you mean n(n+1)/2 ?

But that doesn't apply in this case, does it?

[keen burrow]

Why not

[flint gulch]

Well I tried replacing n with n/2 and my answer ended up being wrong

[keen burrow]

Set n/2 to = m then

m(m+1)/2

What does that =

[flint gulch]

(m^2 + m)/2

[keen burrow]

Try changing the m back to n/2 now

[flint gulch]

(n^2/4 + n/2)/2

Which is n^2/2 + n I think?

[keen burrow]

No

It’s (n^2/2 + n)/4

But now you can put all these equations back into one

n + (your three equations)

Let’s actually keep this so we can put all the number together

[keen burrow]

Here

So it’s n + (n^2 + n + n^2/4 + n/2)/2

Hold on I got something messed up 💀

wait up

Oh it’s - the sum of i

[keen burrow]

So it’s n + (n^2 + n - n^2/4 - n/2)/2

n + n(3n/4 + 1/2)/2

And from checking that is correct

[keen burrow]

Simplify a bit more for

n(1 + (3n/2 + 1)/4)

Or on paper to write it a bit neater

Do you understand everything @flint gulch

[flint gulch]

@keen burrow I'm still confused, because apparently I'm supposed to get (3n^2 + 2n)/2 for the sum

[keen burrow]

Wdym

[flint gulch]

And also when I did all the calculations myself I got (3n^2 + 6n)/8

[keen burrow]

For what sum

[flint gulch]

I mean for the whole sum of n - i + 1

Also I'm representing the result as a trinomial because it's for a time complexity function

[keen burrow]

My answer is correct let me just check if those are also =

[flint gulch]

Alright, it might be the answer in my textbook that's wrong then

Or how I approached the problem

[keen burrow]

This is the only way I get 3n^2

From mine

[keen burrow]

That’s not right

Just try it with any equation and you will find it to be wrong

[flint gulch]

That's why I was so confused

Well, thank you for your help

[keen burrow]

It should = 50 when n is 10

But you get 160

[keen burrow]

You might’ve went wrong somewhere

Cus ur answer is closer

[flint gulch]

I'll check tomorrow but for now it's 1am so I'll just mark this as solved

[keen burrow]

Wait meant to be a plus

[flint gulch]

Thanks again :D

[keen burrow]

Accidentally did -

Yes you must’ve used 2 n instead of 3 n here

[flint gulch]

I think so yeah

[keen burrow]

When you moved it in you should’ve changed the denominator from 1 to 2

[flint gulch]

How do I mark this as solved btw?

[keen burrow]

.solved

[flint gulch]

.solved

[deft charm]

Solved

Post marked as solved by @flint gulch.

Use .unsolved if this was a mistake.

[flint gulch]

Thanks

[keen burrow]

I like sum problems lol

[flint gulch]

I'm glad you do so you can help me lol

Anyway I'm tired so c ya!