Question

n/6!=4/8!+3/6! Find the value of n

Answer 1

Answer:

n/6! -3/6! =4/8!

taking 6! as LCM

n-3/6! =4/8!

n-3 = 4×6!/8!

n-3 = 1/14

n = 43/14

Answer 2

Answer:

The value of n in the given equation is $n=\frac{43}{14}$

Step-by-step explanation:

Given equation is $\frac{n}{6!}=\frac{4}{8!}+\frac{3}{6!}$

To find the value of n in the given equation :

The formula for $n!=n\times (n-1)\times (n-2)...\times 2\times 1$

Put n=6 in the formula

$6!=6\times (6-1)\times (6-2)\times (6-3)\times (6-4)\times (6-5)\times (6-5)$

$6!=6\times 5\times 4\times 3\times 2\times 1$

Similarly we can find $8!=8\times 7\times 6\times 5\times 4\times 3\times 2\times 1$

Now solve the given equation

$\frac{n}{6!}=\frac{4}{8!}+\frac{3}{6!}$

$\frac{n}{6!}-\frac{3}{6!}=\frac{4}{8!}$

$\frac{n-3}{6!}=\frac{4}{8!}$

$n-3=\frac{4(6!)}{8!}$

Now substitute the factorial values in the above equation

$n-3=\frac{4(6\times 5\times 4\times 3\times 2\times 1)}{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}$

$n-3=\frac{1}{14}$

$n=\frac{1}{14}+3$

$=\frac{1+42}{14}$

Therefore $n=\frac{43}{14}$