related to binomial maybe

[jagged steeple]

Let $f(x)= 1-x+x^2-x^3+\cdots+x^{16}-x^{17}= a_0 + a_1 (1+x) + a_2(1+x)^2+ \cdots + a_{17} (1+x)^{17}$, find the value of $a_2$.

[low canyon]

Love

[sly quest]

How would you find a_0?

[jagged steeple]

its 1

i think

nvm

[glad mirage]

you can try finding coefficient of x^2 in f(x-1)

it'll be easier i think

[jagged steeple]

okay

[sly quest]

Btw, do you know what a derivative is?

[jagged steeple]

yes

[sly quest]

Okay, taking those might be useful in problems like these

[jagged steeple]

so with respect to x or (1+x)

[sly quest]

I guess you need to try it

[jagged steeple]

okay

[glad mirage]

you can't really directly differentiate wrt x+1, you have to make a dummy variable
and it's almost the same as substituting x = x-1

derivatives can be useful because coefficient of x^2 in polynomial f(x) is the free term in second derivative of f