Math, asked by elissapandargda, 22 days ago

If 1/7!+1/8!=x/9! , then find the value of x​

Answers

Answered by Anonymous
16

Factorial notation

The notation n! represents the product or first n natural numbers, i.e., the product 1 \times 2 \times 3 \times ...  \times (n - 1) \times n is denoted as n!.

We read n! symbol as 'n factorial'.

Thus, 1 \times 2 \times 3 \times ...  \times (n - 1) \times n = n!

1 = 1!

1 \times 2 = 2!

1 \times 2 \times = 3! and so on.

We can write, 4! = 4 \times 3! = 4 \times 3 \times 2! = 4 \times 3 \times \times 2 \times 1!

Solution:

We are asked to solve for x of the following equation:

\longrightarrow \dfrac{1}{7!} + \dfrac{1}{8!} = \dfrac{x}{9!}

We can write 8! as 8 \times 7!. And 9! as 9 \times 8 \times 7!.

\implies \dfrac{1}{7!} + \dfrac{1}{8 \times 7!} = \dfrac{x}{9 \times 8 \times 7!}

\implies 1 + \dfrac{1}{8} = \dfrac{1}{9 \times 8}

\implies 1 + \dfrac{1}{8} = \dfrac{x}{9 \times 8}

\implies \dfrac{9}{8} = \dfrac{x}{9 \times 8}

\implies \dfrac{9}{8} = \dfrac{x}{72}

\implies 8x = 9 \times 72

\implies 8x = 648

\implies x = 81

Hence, the value of x is 81.

Answered by PeachyRosie
2

Answer :

  • Value of x is 81

Given :

  • If 1/7! + 1/8! = x/9!

To find :

  • Value of x

Solution :

Given

  • 1/7! + 1/8! = x/9!

↝ 1/7! + 1/8! = x/9!

↝ 9!(1/7! + 1/7!) = x

↝ 9!/7! + 9!/8! = x

↝ 9 × 8 × 7! / 7! + 9 × 8! / 8! = x

↝ 9 × 8 + 9 = x

↝ 72 + 9 = x

↝ 81 = x

↝ x = 81

Hence , Value of x is 81.

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