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Series: direct computations

There are two types of series where we can compute the value exactly: geometric series, and series where we can use the "`cancelling trick"'.

  1. $ \sum_{n=0}^\infty \frac{3^{n+1}}{5^{n-1}}$
  2. $ 3 + 2 + \frac 43 + \frac 89 + \frac {16}{27} + \dots$
  3. $ \sum_{k=2}^\infty \frac{4^k}{7^k}$
  4. $ \sum_{k=2}^\infty \frac{7^k}{4^k}$
  5. $ \frac 1{2\cdot 4} + \frac 1{3\cdot 5} + \frac 1{4\cdot 6} + \dots$
  6. $ \sum_{k=2}^\infty \frac 1{\sqrt{k}} - \frac 1{\sqrt{k+1}}$
There may also be one geometric problem related to geometric series, similar to 10.2, 29-32.



Arend Bayer 2006-12-15