can someone help please? i should be quite easy and its so important for me 🥰
#find the sum of the ecuation
delicate gull
median olive
can someone help please? i should be quite easy and its so important for me 🥰
We have:
a(k) = (-1)^k (n + 1)!/(k(k - 2)! (n + 1 - k)!)
Let's multiply and divide by (k - 1), so that we obtain k! int the denominator.
a(k) = (-1)^k (k - 1)(n + 1)!/(k(k - 1)(k - 2)! (n + 1 - k)!) = (-1)^k (k - 1)(n + 1)!/(k!(n + 1 - k)!)
By definition: (n + 1)!/(k!(n + 1 - k)!) = C(n + 1, k).
a(k) = (-1)^k (k - 1)C(n + 1, k)
Can you do it from here?
delicate gull
let me write it on paper please and ill tell you, thanks
median olive
Alright, I'll check what you write.
median olive
Yes.
delicate gull
and idk what to do from here
maybe i can try to remove the (k-1) from the outside?
median olive
Well, now split it in two terms: (-1)^k kC(n + 1, k) - (-1)^k C(n + 1, k).
For both terms, consider the binomial expansion. For the second term, some differentiation will be required.
delicate gull
okeyy
balmy ingot
but how do you split it like that?
median olive
Well, just expand (k - 1).
median olive
Corrected.
delicate gull
ok let me try to do something from here
my friend says something like that
this is correct?
i find it a bit strange
median olive
No, that's not correct. (-1)^k disappeared for some reason.
median olive
Again, what you should do is consider the series for the function (1 + x)^(n + 1).
delicate gull
not gonna lie, im kind of lost rn
i dont know what to do
i dont see the continuation here
median olive
You're welcome!