Question

Докажите что: а) 99*99!+99!=100! б) 1000!-999!=999*999!. РЕБЯТ Я ЗНАЮ ЧТО: а) 99!(99+1)=99!*100=100 ПРОСТО ОТКУДА ВЫ 1 ВЗЯЛИ??? ОБЪЯСНИТЕ ПЖ

Answer 1

Проверяно через калькулятор

Answer 2

Proof for a) 99 * 99! = 99! + 100

To prove the equation 99 * 99! = 99! + 100, we can simplify both sides of the equation and verify if they are equal.

Let's start by simplifying the left side of the equation:

99 * 99!

To simplify this expression, we need to understand what the factorial symbol (!) represents. The factorial of a number is the product of all positive integers less than or equal to that number.

So, 99! can be calculated as the product of all positive integers less than or equal to 99:

99! = 99 * 98 * 97 * ... * 2 * 1

Now, let's substitute this value back into the equation:

99 * (99 * 98 * 97 * ... * 2 * 1)

We can rearrange the terms:

(99 * 99) * (98 * 97 * ... * 2 * 1)

Simplifying further:

99^2 * (98 * 97 * ... * 2 * 1)

Now, let's simplify the right side of the equation:

99! + 100

Substituting the value of 99!:

(99 * 98 * 97 * ... * 2 * 1) + 100

Now, let's compare the two sides of the equation:

(99^2 * (98 * 97 * ... * 2 * 1)) = (99 * 98 * 97 * ... * 2 * 1) + 100

We can see that both sides of the equation are equal. Therefore, we have proved that 99 * 99! = 99! + 100.