E=4*4! + 5*5! + 6*6! ........19*19!
Remainder when E is divided by 64
a)0 b)58 c)others
Answers
Answered by
1
answer :-
correct option is
c)others
explaination :-
Remainder = 40
=> E = 4*4! + 5*5! + 6*6! ........19*19!
=> E = (5-1)*4! + (6-1)*5! + (7-1)*6! ........(20-1)*19!
=> E = (5!-4!)+(6!-5!)+(7!-6!)+.........+(20!-19!)
=> E = (20!-4!)
=> E/64 = (20!-4!)/64
=> rem = 0-24/64 = -24/64
=> rem = -24+64 = 40
Answered by
0
Answer:
The remainder will be -24+64=40.
Step-by-step explanation:
It is given that E=4*4! + 5*5! + 6*6! ........19*19!
We need to determine remainder when E is divided by 64.
As E = 4*4! + 5*5! + 6*6! ........19*19!
We can rearrange it as:
E = (5-1)*4! + (6-1)*5! + (7-1)*6! ........(20-1)*19!
E = (5!-4!)+(6!-5!)+(7!-6!)+.........+(20!-19!)
E = (20!-4!)
We can write
E/64 = (20!-4!)/64
Remainder will be 0-24/64 = -24/64
So remainder will be -24+64=40
#SPJ2
Similar questions