Under what conditions does an alternating series converge? an alternating series ∞ an n = 1 = ∞ (−1)n − 1bn, n = 1 where bn = |an|, converges if 0 < bn + 1 ≤ bn for all n.

First, write the alternate series as where the term is positive. From the Cauchy criterion we already know that . So, in order to  assure the convergence we only need to ask that the term   is monotonically decreasing.

Step-by-step explanation:

This is the Leibniz criterion for the convergence of alternate series.

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743