Proof by induction question, HELPPP

[wintry dagger]

wth is prove by induction 💀

[shell depot]

you know how to do proof by induction?

[solar ermine]

ye

but dunno how to do this

[shell depot]

okay lemme just write it down see if it's any clearer

kind of hard to explain

[solar ermine]

tysm!!

[shell depot]

Then obviously just say, shown true for n=1, assumed true for n=k …

[solar ermine]

oh yeah

thank you so much honestly

[solar ermine]

@shell depot i cant do this one cant figure the algebra part

[shell depot]

ok so for these ones always factor out as much as possible

[solar ermine]

okay ill try that

[shell depot]

$\sum_{r=1}^{n} 6r^3- 5r^2 + r$

[shut grove]

David

[shell depot]

use summation formulas

so we get

$\frac{6n^2(n+1)^2}{4} - \frac{5(n)(n+1)(2n+1)}{6} + \frac{n(n+1)}{2}$

[shut grove]

David

[shell depot]

you can take out a factor of n(n+1)/2 quite nicely

[solar ermine]

but is that induction

[shell depot]

this doesn't seem like an induction question ngl

[solar ermine]

ik but i have to prove by induction

[shell depot]

just same steps

show true for n=1

assume true for n=k

show it's true for n=k+1

when you do n=k+1 though your assumption for the series only holds to n = k