Sum of the Alternating Harmonic Series (I)
Sum of the Alternating Harmonic Series (I)
The graph shows that:
The purple area is .
11-=1-
1
2
1
2
The blue area is -=-.
1
2
2
3
2
4
1
3
1
4
The green area is-+-=-+-.
1
4
4
5
4
6
1
4
4
7
4
8
1
5
1
6
1
7
1
8
The yellow area is -+-+-+-=-+-+-+-.
1
8
8
9
8
10
1
8
8
11
8
12
1
8
8
13
8
14
1
8
8
15
8
16
1
9
1
10
1
11
1
12
1
13
1
14
1
15
1
16
Therefore .
1-+-+-+…==ln2
1
2
1
3
1
4
1
5
1
6
∞
∑
n=1
n+1
(-1)
1
n