Answer:
a) [tex]f(n) = n^{2}[/tex]
[tex]f(1) = 1[/tex], [tex]f(2) = 4[/tex], [tex]f(3) = 9[/tex], [tex]f(4) = 16[/tex], [tex]f(5) = 25[/tex]
b) [tex]f(n) = n^{3}[/tex]
[tex]f(1) = 1[/tex], [tex]f(2) = 8[/tex], [tex]f(3) = 27[/tex], [tex]f(4) = 64[/tex], [tex]f(5) = 125[/tex]
c) [tex]f(n) = n^{2}+n^{3}[/tex]
[tex]f(1) = 2[/tex], [tex]f(2) = 12[/tex], [tex]f(3) = 36[/tex], [tex]f(4) = 80[/tex], [tex]f(5) = 150[/tex]
Step-by-step explanation:
This formulas uses only natural numbers, which means that [tex]n \ge 1[/tex]. Then, we evaluate each function at 1, 2, 3, 4 and 5:
a) [tex]f(n) = n^{2}[/tex]
[tex]f(1) = 1[/tex], [tex]f(2) = 4[/tex], [tex]f(3) = 9[/tex], [tex]f(4) = 16[/tex], [tex]f(5) = 25[/tex]
b) [tex]f(n) = n^{3}[/tex]
[tex]f(1) = 1[/tex], [tex]f(2) = 8[/tex], [tex]f(3) = 27[/tex], [tex]f(4) = 64[/tex], [tex]f(5) = 125[/tex]
c) [tex]f(n) = n^{2}+n^{3}[/tex]
In which each element is the sum of respective results found in a) and b).
[tex]f(1) = 2[/tex], [tex]f(2) = 12[/tex], [tex]f(3) = 36[/tex], [tex]f(4) = 80[/tex], [tex]f(5) = 150[/tex]
