Practice question · Numerical answer
A geometric series starts at n = 0 with ratio r = 0.2. What does it sum to?
Hints
- Use 1 divided by (1 - r).
- 1 - 0.2 = 0.8.
Show the answer
1.25 (answers within ±0.001 count)
Why
1 divided by 0.8 is 1.25. Note how much smaller this is than the r = 0.5 case, which sums to 2: the closer the ratio sits to 1, the more slowly the series converges and the more terms a computer must add for a given accuracy.
Practise Sequences and Series
The app has 6 more questions on this lesson, and keeps your place in the course. Computer Science I is free to start.
More questions on Sequences and Series
- Monte Carlo integration is hopeless in one dimension and indispensable in three hundred. What flips the…
- An infinite series with terms tending to zero may still diverge - the harmonic series does. Why is "the terms…
- Sort each series by whether it converges.
- The terms of a series shrinking toward zero is not enough to make the series converge.