Latest Bank Exam Aptitude Question SOLUTION: Prove that 0! = 1 (please solve with explanation)

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(#M40034501) BANK EXAM Numerical Ability question Keep an EYE

Prove that 0! = 1
(please solve with explanation)

Asked In Bank Exam Aashu (10 years ago)

Solved S.SHAFI Read Solution (4)

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Read Solution (4) :

S.SHAFI  (10 years ago)

n! = n*(n-1)*(n-2)*(n-3)*....*3*2*1

The above formula can be written as
n! = n*(n-1)!, then

(n-1)! = n!/n

Put n=1, then 0! = 1!/1 = 1

Is this solution Helpfull? Yes (5) | No (1)  

virendra dubey  (10 years ago)

as n!=n*(n-1)*....*1;
so n!=n*(n-1)!
hence n!/(n-1)!=n;
put n=1;
so 1!/(1-1)!=1;
1!/0!=1;
1!/1=0! so 0!=1 hence proved

Is this solution Helpfull? Yes (2) | No   

Akanksha Mishra  (10 years ago)

Usually n factorial is defined in the following way:

n! = 1*2*3*...*n
But this definition does not give a value for 0 factorial, so a natural question is: what is the value here of 0! ?

A first way to see that 0! = 1 is by working backward. We know that:

1! = 1
2! = 1!*2
2! = 2
3! = 2!*3
3! = 6
4! = 3!*4
4! = 24


We can turn this around:
4! = 24
3! = 4!/4
3! = 6
2! = 3!/3
2! = 2
1! = 2!/2
1! = 1
0! = 1!/1
0! = 1

Is this solution Helpfull? Yes (1) | No (3)  

ram kiran  (10 years ago)

(n-1)! = n!/n
0!=1!/1
1!=2!/2
and so on ...........

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