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ਕਦਮ ਦਰ ਕਦਮ

1. \sum_{n=1}^{\infty} 2^{- n} n

   Does this series converge?

2. \lim_{n\to\infty} 2^{- n} n = 0

   Divergence test: if the terms do not go to 0 the series cannot converge.

3. \lim \left|\frac{a_{k+1}}{a_k}\right| = \lim \frac{\left|{\frac{n + 1}{n}}\right|}{2} = \frac{1}{2}

   Ratio test: < 1 converges, > 1 diverges, = 1 says nothing.

4. = 2

   It converges, and the CAS knows the sum.