The limit of the sequence defined by \( s_n = \sum_{k=1}^{n} \left(\frac{1}{3}\right)^k \) converges to 1 as \( n \) approaches infinity. This sequence represents a geometric series where the first term is \( \frac{1}{3} \) and the common ratio is also \( \frac{1}{3} \). The formula for the sum of a geometric series can be applied here, confirming that the limit is indeed 1. Understanding the notation and the properties of geometric series is essential for grasping this concept.
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teng125 said:Determine the limit of the sequence (sn)n=N given by
n(sum)k=1 (1/3)^k , n is natural numbers.
i don't understand what is the meaning
can anyonepls help...thanx