You are asked to prove that the series 1/2 + 1/3 + 1/5 + 1/7 + 1/11 + , containi

Question

You are asked to prove that the series 1/2 + 1/3 + 1/5 + 1/7 + 1/11 + , containing all the inverses of the prime numbers is divergent. This is the basis of Euler's argument that there are infinitely many prime numbers. Follow the following steps. Show that if p is any prime number, 1/1 - 1/p - 1+ 1/p + 1/p2 + 1/p3 + Use the previous equality to show that if pn is the nth prime number, 1/1 - 1/2, 1/1 - 1/3, , 1/1 - 1/pn 1/k Draw a figure similar to the one in the integral test to shows that Deduce that (1 - 1/2)(1 - 1/3) (1 - 1/pn)

Explanation / Answer

can you pls apply mathematical induction.its too clumsy for me to do here. if you can wait i can upload on a picture.Please rate meanwhile.Thanks :)

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