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Representation of series

Suppose we have a sequence with , whose terms are real numbers. For each , we define the partial sum

of the first terms of . Thus we obtain a new sequence , with . The following simulation shows the approximate values of the partial sums , from 1 to 1000 terms. Things to try:

  • Drag the slider n to explore the values of .
  • Change the function that define the series.
  • Example: (-1)^(n+1)/n
  • Example: n*sin(sqrt(n+1))