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Celmaun · Answer 1 · 2023-09-23T03:27:15+0000

We are asked to evaluate each of the expressions for n = 1, 2, 3, 4

We simply need to substitute the value of n into the expression and simplify the expression.

Expression 1:

$\begin{gathered} for\; n=1\colon\; \; 4n-1=4(1)-1=4-1=3 \\ for\; n=2\colon\; \; 4n-1=4(2)-1=8-1=7 \\ for\; n=3\colon\; \; 4n-1=4(3)-1=12-1=11 \\ for\; n=4\colon\; \; 4n-1=4(3)-1=16-1=15 \end{gathered}$

Expression 2:

$\begin{gathered} for\; n=1\colon\; \; 3-n^2=3-(1)^2=3-1=2 \\ for\; n=2\colon\; \; 3-n^2=3-(2)^2=3-4=-1 \\ for\; n=3\colon\; \; 3-n^2=3-(3)^2=3-9=-6 \\ for\; n=4\colon\; \; 3-n^2=3-(4)^2=3-16=-13 \end{gathered}$

Expression 3:

$\begin{gathered} for\; n=1\colon\; \; (1)/(n-2)=(1)/(1-2)=(1)/(-1)=-1 \\ for\; n=2\colon\; \; (1)/(n-2)=(1)/(2-2)=(1)/(0)=\text{undefined} \\ for\; n=3\colon\; \; (1)/(n-2)=(1)/(3-2)=(1)/(1)=1 \\ for\; n=4\colon\; \; (1)/(n-2)=(1)/(4-2)=(1)/(2)=0.5 \end{gathered}$

Expression 4:

$\begin{gathered} for\; n=1\colon\; \; (n^2)/(n-1)=((1)^2)/(1-1)=(1)/(0)=\text{undefined} \\ for\; n=2\colon\; \; (n^2)/(n-1)=((2)^2)/(2-1)=(4)/(1)=4 \\ for\; n=3\colon\; \; (n^2)/(n-1)=((3)^2)/(3-1)=(9)/(2)=4.5 \\ for\; n=4\colon\; \; (n^2)/(n-1)=((4)^2)/(4-1)=(16)/(3)=5.3 \end{gathered}$

Expression 5:

$\begin{gathered} for\; n=1\colon\; \; 2n+4=2(1)+4=2+4=6 \\ for\; n=2\colon\; \; 2n+4=2(2)+4=4+4=8 \\ for\; n=3\colon\; \; 2n+4=2(3)+4=6+4=10 \\ for\; n=4\colon\; \; 2n+4=2(4)+4=8+4=12 \end{gathered}$

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