Alternating Series Test Calculator

Apply Leibniz's rule to sequences

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Select Sequence Pattern bₙ

The calculator automatically prepends the (-1)ⁿ alternating sign internally.

Starting Term Index (n₀)

∞n=1

Σ(-1)ⁿ·1/n

Series Converges ✅

Both criteria of the Alternating Series Test are satisfied.

✅

Condition 1: Limit approaches zero

lim(n→∞) bₙ ≈ 0

✅

Condition 2: Monotonically Decreasing

bₙ₊₁ ≤ bₙ (Sampled: 1.000 → 0.500 → 0.333)

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About Alternating Series Test Calculator

The Alternating Series Test states that an alternating infinite sequence converges if its absolute terms strictly decrease and the limit approaches zero. Select a standard sequence template to safely approximate convergence mathematically without drawing out complex proof tables.

Alternating Series Test Calculator Features

Verifies monotonically decreasing items
Calculates limit n->∞ assumptions
Preconfigured alternating signs

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