Question

Let Hn define the sum of reciprocals of all integers from 1 to n:
Hn = 1 +
1
2
+
1
3
+
1
4
+ ... +
1
n
Prove the following identity:
H2n − Hn = 1 −
1
2
+
1
3
−
1
4
± ... +
1
2n − 1
−
1
2n