Respuesta :
In the given figure:
step 1 has 2 blocks
step 2 has 6 blocks
step 3 has 12 blocks
1)
[tex]\begin{gathered} n^2+1 \\ \text{for step1, n =1} \\ 1^2+1=2 \\ \text{for step2, n=2} \\ 2^2+1=5 \\ \text{ but in step 2, there are 6 blocks} \\ \text{ So, expression: n}^2+1\text{ is not valid} \end{gathered}[/tex]2) n( n + 1 )
[tex]\begin{gathered} \text{ for step 1, n=1} \\ n(n+1) \\ 1(1+1)_{} \\ 1(2)=2 \\ \text{Step 1 has two blocks} \\ \text{for step 2, n=2} \\ n(n+1)=2(2+1) \\ n(n+1)=2(3) \\ n(n+1)=6 \\ \text{step 2 has 6 blocks} \\ \text{for step 3, }n=3 \\ n(n+1)=3(3+1) \\ n(n+1)=3(4) \\ n(n+1)=12 \\ \text{ step 3 has 12 blocks} \\ \text{Thus, expression : n(n+1) is valid} \end{gathered}[/tex]n( n + 1 ) is valid
3)
[tex]n^2+n[/tex]Since the expression can also write as:
[tex]n^2+n=n(n+1)[/tex]Thus, n^2 +n is also valid
4)
[tex]\begin{gathered} n+n+1 \\ \text{for step 1, n = 1} \\ 1+1+1=3 \\ \text{but step 1 has 2 block not 3,} \\ \text{thus, the expression is not valid} \end{gathered}[/tex]n + n + 1 is not valid
Answer :
b) n( n + 1 )
c) n^2 + n
