SOLUTION: Let n be a positive integer, k the number of prime numbers less than or equal to n, and {{{p[k]}}} the greatest prime number less than or equal to n. Prove that {{{1/p[1]+1/p[2

Algebra ->  Divisibility and Prime Numbers -> SOLUTION: Let n be a positive integer, k the number of prime numbers less than or equal to n, and {{{p[k]}}} the greatest prime number less than or equal to n. Prove that {{{1/p[1]+1/p[2      Log On


   

Question 1027346: Let n be a positive integer, k the number of prime numbers less than or equal to n, and p%5Bk%5D the greatest prime number less than or equal to n. Prove that
1%2Fp%5B1%5D%2B1%2Fp%5B2%5D%2B1%2Fp%5B3%5D+...+1%2Fp%5Bk-1%5D%2B1%2Fp%5Bk%5D+%3E+%282n%29%2F%28n%2B1%29,
where p%5B1%5D, p%5B2%5D, p%5B3%5D, ...,p%5Bk-1%5D, and p%5Bk%5D are the k prime numbers less than or equal to n.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Is that even true?

For example, if n = 10, then we have



which is a false statement.