$$\sum_{k=1}^n (1/2)$$
Why/how does this series diverge?
Why doesn't it converge?
2026-03-26 14:17:44.1774534664
Testing for divergence and convergence
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$$ S(n) = \sum_{k=1}^n (1/2) = (1/2)\sum_{k=1}^n 1 = (1/2) n $$ Given any real number $y > 0$ we see that $$ S(n) = (1/2) n > y \iff n > 2y $$ So we choose $n_0 = 2 \lceil y \rceil$ and then for all $n \ge n_0$ we have $S(n) > y$. This means $$ \lim_{n\to\infty} S(n) = \infty $$