algebraic proof

[placid wadi]

(n+1)^2 - (n)^2 = 2n+1

[cold star]

could you tell me how you got taht

@placid wadi can u help me with this?

[placid wadi]

If (n) is an integer then (n+1) is the next integer. From there you just square your two arbitrary integers and subtract them.

[cold star]

is that for the new one i just sent

[cold star]

this one?

[placid wadi]

No it's the 1st one

[cold star]

can you help on the second one

ive already gone past it

ill be back in 10

back

[signal violet]

The sum of any two consecutive terms is $4n-10+4n-6=8n-16=8(n-2)$.

[normal gale]

Civil Service Pigeon

[cold star]

@signal violet

[loud bane]

(n+3)^2 - (n-3)^2 = ( (n+3) + (n-3) ) ( (n+3) - (n-3) ) = 2n * 6 = 12n
We use the a^2 - b^2 = (a-b)(a+b) formula here

12n is even for all positive integer values of n, it's kinda obvious

[cold star]

didnt work

i got it wrong

[cold star]

can u help with this

[loud bane]

What exactly didn't work?

[cold star]

its wrong

[loud bane]

it actually can't be wrong 0-0

[cold star]

1st one is 12n i agree, but the computer said its wrong

[cold star]

thank u