1
answer
0
watching
130
views
6 Oct 2020
Prove that if n > 1, the nth partial sum of the harmonic series is not an integer. Hint: Let be the largest power of 2 that is less than or equal to n and let M be the proudct of all odd integers that are less than or equal to n. Suppose that an integer. Then . The right side of this equation is even. Prove that the left side is odd by showing that each of its terms is an even integer, except for the last one.
Prove that if n > 1, the nth partial sum of the harmonic series is not an integer. Hint: Let be the largest power of 2 that is less than or equal to n and let M be the proudct of all odd integers that are less than or equal to n. Suppose that an integer. Then . The right side of this equation is even. Prove that the left side is odd by showing that each of its terms is an even integer, except for the last one.
1
answer
0
watching
130
views
For unlimited access to Homework Help, a Homework+ subscription is required.
Priyanshu PatelLv10
26 Jan 2021