Latest TCS Aptitude Question SOLUTION: 1! + 2! + ��. + 50!=?

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(#M40040315) TCS Numerical Ability question Keep an EYE

1! + 2! + ��. + 50!=?

Asked In TCS bhagwandas kushwaha (9 years ago)

Unsolved Read Solution (4)

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Read Solution (4) :

Anuj Yadav  (9 years ago)

I think there is no such shortcut but if you provide options then it can be solve easily by just finding unit digit...

For example in above question:

1! = 1 (units digit 1)
2! = 2 (units digit 2)
3! = 6 (units digit 6)
4! = 24 (units digit 4)
5!, 6!.... the units digit will be 0 because all the terms will include 5x2=10

units digit of 1!+2!+... will be 1+2+6+4+0+0+0.... = 3

Hence the answer should contain unit digit as 3.



Or you can try(I m not sure)
Use (n+1)!=(n+1)⋅n!=n⋅n!+n!.

Is this solution Helpfull? Yes (29) | No (1)  

Nirmalya Basu  (9 years ago)

There are no such shortcuts for finding the summation of a factorial series. But if you know the factorial of the last number it helps.
50! is 30414093201713378043612608166064768844377641568960512000000000000
(Of course I used calculator for it)

now rearranging the series as
50!+49!+48!+.....+1!
= 50!(1+1/50+1/(50*49)+1/(50*48*49)+1/(50*48*49*47).....)(ignoring the rest due to extremely small values.
=50!(1+0.02+0.00040816326+0.0000085034+...)
=50!*1.020409
=3.1034814e+64

Which is not 100% accurate, but is 99.9% accurate.

Is this solution Helpfull? Yes (6) | No   

Koushik Das  (9 years ago)

1!+2!+3!+...............................50!
=50!*(1!/50! + 2!/50! + ........................49!/50!+1)
=50!*(1+49!/(50*49!) + 48!/(50*49*48!) + ........................................+1!/50!)
=50!*(1+1/50+1/(50*49)+...................................................)
=50!*(1+0.02) (Taking the 1st 2 terms rest of the terms are neglegible)
=1.02*50!

Is this solution Helpfull? Yes (1) | No   

kundan karn   (9 years ago)

SUM=l/2(a+l)
=50!/2(1!+50!)
=50!*51!/2

Is this solution Helpfull? Yes | No (3)  

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