Harmonic Sequence Task
The Harmonic Series
The Harmonic series is the sequence of
running totals, or partial
sums of the reciprocals. That might sound scary, but its really
quite simple. A partial sum of an infinite sequence is the sum of all
terms of the sequence up to a point. In the case of the reciprocals (1, 1/2,
1/3, 1/4) this would be:
or 1+1/2,
or 1+1/2+1/3,
or 1+1/2+1/3+1/4,
etc.
These partial sums are themselves a sequence:
Which is sometimes written as:
Generate the harmonic series
Follow the instructions in the box below
to create a robot for the harmonic series. Post the robot you trained instead
of this box.
Post the first few terms of the Harmonic series
in a box here:
Predict
Fill in the table:
| Will the Harmonic series reach..? |
Predict: yes / no |
Predict: If yes, how big will the Denominator be? |
Test: Were you right? |
|---|---|---|---|
| 2 |
|||
| 5 |
|||
| 7 |
|||
| 10 |
|||
Do you think that the Harmonic series
Converges or Diverges?
Imagine a classmate thinks the opposite. Convince them of your opinion: