Solve frac{1.8^{0}e^{-1.8}}{0!}+1.8^1e^-1.8/1!+1.8^2e^-1.8/2!

$$\frac { 1.8 ^ { 0 } e ^ { - 1.8 } } { 0 ! } + \frac { 1.8 ^ { 1 } e ^ { - 1.8 } } { 1 ! } + \frac { 1.8 ^ { 2 } e ^ { - 1.8 } } { 2 ! }$$

Evaluate

$$\frac{221}{50e^{1.8}}\approx 0.730621086$$

Solution Steps

Calculate 1.8 to the power of 0 and get 1.

$$\frac{1e^{-1.8}}{0!}+\frac{1.8^{1}e^{-1.8}}{1!}+\frac{1.8^{2}e^{-1.8}}{2!}$$

The factorial of 0 is 1.

$$\frac{1e^{-1.8}}{1}+\frac{1.8^{1}e^{-1.8}}{1!}+\frac{1.8^{2}e^{-1.8}}{2!}$$

Cancel out 1 and 1.

$$e^{-1.8}+\frac{1.8^{1}e^{-1.8}}{1!}+\frac{1.8^{2}e^{-1.8}}{2!}$$

Calculate 1.8 to the power of 1 and get 1.8.

$$e^{-1.8}+\frac{1.8e^{-1.8}}{1!}+\frac{1.8^{2}e^{-1.8}}{2!}$$

The factorial of 1 is 1.

$$e^{-1.8}+\frac{1.8e^{-1.8}}{1}+\frac{1.8^{2}e^{-1.8}}{2!}$$

Anything divided by one gives itself.

$$e^{-1.8}+1.8e^{-1.8}+\frac{1.8^{2}e^{-1.8}}{2!}$$

Combine e^{-1.8} and 1.8e^{-1.8} to get 2.8e^{-1.8}.

$$2.8e^{-1.8}+\frac{1.8^{2}e^{-1.8}}{2!}$$

Calculate 1.8 to the power of 2 and get 3.24.

$$2.8e^{-1.8}+\frac{3.24e^{-1.8}}{2!}$$

The factorial of 2 is 2.

$$2.8e^{-1.8}+\frac{3.24e^{-1.8}}{2}$$

Divide 3.24e^{-1.8} by 2 to get 1.62e^{-1.8}.

$$2.8e^{-1.8}+1.62e^{-1.8}$$

Combine 2.8e^{-1.8} and 1.62e^{-1.8} to get 4.42e^{-1.8}.

$$4.42e^{-1.8}$$