write the remainder obtained when 1!+2!+3!+........+200! is divided by 14
Asked by devashree | 7th Jan, 2014, 03:13: PM
Expert Answer:
1! + 2! + 3! + 4! + 5! + ……….. + 200!
All the terms starting from 7! are divisible by 14.
[7! = 7 × 6 × 5! which is divisible by 14, 8! = 8 × 7!]
The remainder obtained when 1! + 2! + 3! + ….. + 200! is divided by 14 would be same as the remainder obtained when 1! + 2! + 3! + 4! + 5! + 6! is divided by 14.
1! + 2! + 3! + 4! + 5! + 6! = 1 + 2 + 6 + 24 + 120 + 720 = 873.
The remainder when 873 is divided by 14 is 5.
Thus, the remainder obtained when 1! + 2! + 3! + …… + 200! is divided by 14 is 5.
1! + 2! + 3! + 4! + 5! + ……….. + 200!
All the terms starting from 7! are divisible by 14.
[7! = 7 × 6 × 5! which is divisible by 14, 8! = 8 × 7!]
The remainder obtained when 1! + 2! + 3! + ….. + 200! is divided by 14 would be same as the remainder obtained when 1! + 2! + 3! + 4! + 5! + 6! is divided by 14.
1! + 2! + 3! + 4! + 5! + 6! = 1 + 2 + 6 + 24 + 120 + 720 = 873.
The remainder when 873 is divided by 14 is 5.
Thus, the remainder obtained when 1! + 2! + 3! + …… + 200! is divided by 14 is 5.
Answered by | 7th Jan, 2014, 10:11: PM
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