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If N is a prime number which divides S=^(39)P_(19)+^(38)P_(19)+^(37)P_(19)+…+"^(20)P_(19), then the largest possible value of N among following is |
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Answer» `41` `=19!{'^(30)C_(19)+^(38)C_(19)+^(37)C_(19)+....+^(20)C_(19)}` `=19!{'^(39)C_(19)+^(38)C_(19)+^(37)C_(19)+....+('^(20)C_(19)+^(20)C_(19))-1}` `=19!{'^(39)C_(19)+^(38)C_(19)+....+('^(21)C_(19)+^(21)C_(19))-1}` `=19!{'^(40)C_(20)-1}` `=((41-1)(41-2)(41-3).....(41-20)-20!)/(20)=(41k)/(20)` `implies` greatest PRIME number is `41` |
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