Nested Factorials!
2 ! + 2 ! + 2 ! + 2 ! + … 2 ! 2 ! 2 ! find value of this expression.
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2 solutions
Upvoted !!!
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Thanx...i guess this is the simpliest way....isn't it
Can anyone please justify why x cannot be negative ?
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Its because all the numbers here are positive.and the sum of positives has to be positive.
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ohh..kk thats what i was thinking.. you're sure there is no other reason ??
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@Rishabh Tripathi – No one knows math completely...can have a different reason as welll
Cannot square root a negative number in the real number system.
I do not see how the factorials go away on line 3. Can you explain?
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Here
2!
has been replaced with
2
.
because
2! = 2x1 = 2
It's easy bro,
n ! = n ( n − 1 ) ( n − 2 ) ( n − 3 ) . . . . . . 3 × 2 × 1
So,
2 ! = 2 × 1 = 2
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Hahah how could I be so silly, thank you Sakanksha.
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@Dylan Scupin-Dursema – There's no need to thank me......i guess we are here to help each other...isn't it.
try these questions - QuEsTiOnS
I did it in the same process !! Simply best process :)
The above can be rephrased as 2/x+2=x. (If the above expression=x)
Which implies that x 2 -2x-2=0
Solving we get two roots 1+√3 & 1-√3 As the later is negative the answer is 1+√3
Let,
x = 2 ! + 2 ! + 2 ! + . . . . . 2 ! 2 !
or,it can be written as,
x = 2 + 2 + 2 + . . . . 2 2
or,
x = 2 + x 2
or,
x 2 = 2 x + 2
Now,by using the quadratic formula,
x = 2 2 + 4 + 8 ; 2 2 − 4 + 8
or,
x = 1 + 3 ; 1 − 3
Now,
Since x cannot be a negative
Therefore,
x = 1 + 3