Leibniz Criterion for Alternating Series
Leibniz Criterion for Alternating Series
An alternating series converges if ≥≥…>0 and =0. Even partial sums = form an increasing sequence and odd partial sums = form a decreasing sequence; their limit is the same.
∞
∑
n=1
n
(-1)
a
n
a
1
a
2
lim
n∞
a
n
S
2N
2N
∑
n=1
n
(-1)
a
n
S
2N-1
2N-1
∑
n=1
n
(-1)
a
n