# 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