This is Series and i need help in these 2 questions for hw

[red stirrup]

plz help guys thx if u cant see smth clearly plz tell imma tell u !~

[lilac badge]

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[red stirrup]

also like plz send pic of calculation if u can

[pale bloom]

Note that the sum of first powers from 1 to n is n(n + 1)/2 and the sum of squares from 1 to n^2 is n(n + 1)(2n + 1)/6. You can prove by induction, by solving a recurrence relation, etc. Whatever you prefer.
As for the second one, you can analyze this sequence using differences. That will allow you to find its formula.

[red stirrup]

I've tried but i keep getting the wrong answer

[pale bloom]

Can you show what you did?

[red stirrup]

i asked chatgpt

[pale bloom]

Uh...

[red stirrup]

yea ik

[pale bloom]

Don't do that. Try doing it yourself.

[red stirrup]

okayyy

imma try and ask u again

@pale bloom hellooo

is this right?

[pale bloom]

We are evaluating the sum of k^2 + k. Where did the 1 come from?

[red stirrup]

oh shit

can u solve it for me

TT^TT

[pale bloom]

Try it yourself. I mean, you just wrote an erroneous 1, so do it without it.

[red stirrup]

okayyy

[pale bloom]

The approach is correct, you just included 1 accidentally.

[red stirrup]

oh so the answer is right?

wait lemme chek

the answer key says its right

[pale bloom]

No. The approach is correct, but the answer isn't.

[pale bloom]

Your current answer isn't even one of the options, though...

[red stirrup]

it is

the 2nd one

of 36

[pale bloom]

No.

Can you show what you did?

[red stirrup]

uh i showed u?

[pale bloom]

What you showed is incorrect. Show the corrected solution.

[red stirrup]

oh like answer key?

[pale bloom]

No.

Show your solution, but without the mistake.

[red stirrup]

ohk

but like the mistake does not matter

my answer is coming correct

[pale bloom]

No.

[pale bloom]

Your answer here is incorrect, and it's not even one of the options.

[red stirrup]

wait lemme show u

its in 2nd img

if i just multiply it i shld be good

hmm

[pale bloom]

Oh. You're solving that problem!

I thought you were solving the first one 😅

[red stirrup]

xDDDDD

its alr

[pale bloom]

Yeah, if it's that, then that's correct. The general term is a(n) = n^2 + n + 1, and the sum is S(n) = (1/3)n(n^2 + 3n + 5).

What about the first, then?

[red stirrup]

yea uh thats not working out well for me

can u solve for me

plzzzz

[pale bloom]

What's the problem, though? It's the same as the second one, but with an even simpler term: a(n) = n^2 + n.

The approach is exactly the same.

[red stirrup]

aight

imma try doing it

aight bro i got it

tyyy~

[pale bloom]

What did you get?

[red stirrup]

1st one

in 1st img

tysm dude

imma close post now

[pale bloom]

Yeah, nice!

You're welcome!