please helpp

[gloomy token]

I'm not 100% on this at all but I think I understand

Which part don't you get

[gloomy token]

right, so i think part 1 is saying,
Consider the set {1,2,3,4,5}
give me a subset, of length 3, which doesnt have any 2 consecutive integers

so, 1,2,4 is not allowed

as 1 and 2 are consecutive

but 1,3,5 is

i think its the only one actually

now the function U(n, k) is asking how many of these subsets we can actually make which follow that rule

so for U(5,3) [our part 1] the answer is 1

so for U(n, 1) , we can only choose one number from our set,
there are n numbers to choose from so the answer is just n

U(n,1)=n

for U(n,2) i think its a lil trickier

lmk if you follow so far

[static nest]

For U(n,2) how we do

@gloomy token

[gloomy token]

Okay, for u(n,2) I think we may need to try some cases.
If n =2, then we have no solutions, as both would have to be chosen, but since they're consecutive wouldn't be allowed

If n=3, U(n,2) = 1, the only solution is 1,3

If n=4 U(n, 4) = 3
1,3 2,4 1,4

Let's try one more

N= 5, u(n, 5)
1,3 1,4 1,5 2,4 2,5 3,5
=6

Think you can go from here?

[static nest]

Thanks a lot

You are the goat

[gloomy token]

Np

[supple kettle]

.solved