Solve 73!+1!/2*73!-1!/1+1=?=?

$$\frac { 73 ! + 1 ! } { 2 } \cdot \frac { 73 ! - 1 ! } { 1 } + 1 = ? = ?$$

Evaluate

$$\frac{19981932239254758918924051339113909793193240033431321836043979426832968801195595658034349202401464677180500630732895618977065149823562487835610850829791647507279219584098854397542400000000000000000000000000000001}{2}\approx 9.99096612 \cdot 10^{210}$$

Solution Steps

The factorial of 73 is 4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000000.

$$\frac{4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000000+1!}{2}\times \frac{73!-1!}{1}+1$$

The factorial of 1 is 1.

$$\frac{4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000000+1}{2}\times \frac{73!-1!}{1}+1$$

Add 4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000000 and 1 to get 4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000001.

$$\frac{4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000001}{2}\times \frac{73!-1!}{1}+1$$

The factorial of 73 is 4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000000.

$$\frac{4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000001}{2}\times \frac{4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000000-1!}{1}+1$$

The factorial of 1 is 1.

$$\frac{4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000001}{2}\times \frac{4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000000-1}{1}+1$$

Subtract 1 from 4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000000 to get 4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903679999999999999999.

$$\frac{4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000001}{2}\times \frac{4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903679999999999999999}{1}+1$$

Anything divided by one gives itself.

$$\frac{4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000001}{2}\times 4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903679999999999999999+1$$

Express \frac{4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000001}{2}\times 4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903679999999999999999 as a single fraction.

$$\frac{4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000001\times 4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903679999999999999999}{2}+1$$

Multiply 4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000001 and 4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903679999999999999999 to get 19981932239254758918924051339113909793193240033431321836043979426832968801195595658034349202401464677180500630732895618977065149823562487835610850829791647507279219584098854397542399999999999999999999999999999999.

$$\frac{19981932239254758918924051339113909793193240033431321836043979426832968801195595658034349202401464677180500630732895618977065149823562487835610850829791647507279219584098854397542399999999999999999999999999999999}{2}+1$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{19981932239254758918924051339113909793193240033431321836043979426832968801195595658034349202401464677180500630732895618977065149823562487835610850829791647507279219584098854397542399999999999999999999999999999999}{2}+\frac{2}{2}$$

Since \frac{19981932239254758918924051339113909793193240033431321836043979426832968801195595658034349202401464677180500630732895618977065149823562487835610850829791647507279219584098854397542399999999999999999999999999999999}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

$$\frac{19981932239254758918924051339113909793193240033431321836043979426832968801195595658034349202401464677180500630732895618977065149823562487835610850829791647507279219584098854397542399999999999999999999999999999999+2}{2}$$

Add 19981932239254758918924051339113909793193240033431321836043979426832968801195595658034349202401464677180500630732895618977065149823562487835610850829791647507279219584098854397542399999999999999999999999999999999 and 2 to get 19981932239254758918924051339113909793193240033431321836043979426832968801195595658034349202401464677180500630732895618977065149823562487835610850829791647507279219584098854397542400000000000000000000000000000001.

$$\frac{19981932239254758918924051339113909793193240033431321836043979426832968801195595658034349202401464677180500630732895618977065149823562487835610850829791647507279219584098854397542400000000000000000000000000000001}{2}$$