Untitled Quiz

Sequences and Series

Exercise 5: Checking Sequences

• Check whether the sequence is bounded, monotonic, and if the limit exists.
• Two sequences to check:
  • ${\frac{3n}{n+2n}}_{n=1}^{\infty}$
  • ${\frac{2^n}{1+2^n}}_{n=0}^{\infty}$

Exercise 6: Determining Subsequences

• Determine three subsequences of each sequence.
• Four sequences to determine subsequences for:
  • {$n}_{n=1}^{\infty}$
  • {$\frac{1}{n}}_{n=1}^{\infty}$
  • ${\frac{3n}{n+2n}}_{n=1}^{\infty}$
  • ${\frac{n}{2n}}_{n=1}^{\infty}$

Exercise 7: Partial Sums of Series

• Determine the fourth partial sum $S_4$ of the series.
• Two series to find the fourth partial sum for:
  • $\sum\limits_{n=0}^{\infty} (n+1)$
  • $\sum\limits_{n=0}^{\infty } ln n$