video example the alternating harmonic series 1 - 1/2 + 1/3 - 1/4 +... = ∑((-1)^(n - 1)/n) from n = 1 to ∞…
video example the alternating harmonic series 1 - 1/2 + 1/3 - 1/4 +... = ∑((-1)^(n - 1)/n) from n = 1 to ∞ satisfies the following. (i) b_n + 1 > b_n because 1/(n + 1) < 1/n (ii) lim(n→∞) b_n = lim(n→∞) 1/n = so the series is convergent by the alternating series test. need help? read it
Answer
Explanation:
Step1: Recall limit rule
We know that for the function $y = \frac{1}{n}$, as $n$ approaches infinity, the value of the function gets smaller and smaller.
Step2: Calculate the limit
The limit $\lim_{n\rightarrow\infty}\frac{1}{n}=0$. This is because as $n$ becomes extremely large, the denominator of the fraction $\frac{1}{n}$ is very large, and the value of the fraction approaches 0.
Answer:
0