Question

f(1) = 35, f(n) = f(1) + f(n-1) for n > 1
Use the recursive formula to make a table of values for 1 ≤ n ≤ 5. Show your calculations. Explain what your table means.

Answer 1

please note that:
\[f(2)=f(1)+f(1)=2f(1)\]
\[f(3)=f(1)+f(2)=f(1)+2f(1)=3f(1)\]
so I congecture this:
\[f(n)=nf(1)(*)\]
and I suppose it is valid, now for n+1, we have:
\[f(n+1)=f(1)+f(n)=f(1)+nf(1)=(n+1)f(n)\]
so (*) it is valid for all n such that:
\[\forall n \in \mathbb{N},n \ge1\]

Answer 2

Okay thanks.

Answer 3

thanks!

Answer 4

f(1)=35;
f(2)=2*f(1)=70
please continue

Answer 5

f(3)=3*f(1)=....