Help
Options
Didn't know it?
click below
click below
Knew it?
click below
click below
Don't Know
Remaining cards (0)
Know
retry
shuffle
restart
0:00
Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.
Normal Size Small Size show me how
Normal Size Small Size show me how
BC Calc - Unit 10
| Question | Answer |
|---|---|
| Recursive Sequence | each term in the sequence is three more than the preceding // a₁=1, a₂=a₁+3, a₃=a₂+3, ... // we should say "a₁=1" and "aₙ₊₁=aₙ+3" where n=1,2,3,... |
| When Writing A Recursive Definition Of A Sequence, Include... | an initial condition (ex: a₁=1) |
| Explicit Sequence | each term in a sequence can be represented by the ordered pairs (order of term, actual value of term) // find relationship between terms and set up an equation (ex: if terms have liner relationship, use y=mx+b) |
| Limit Of A Sequence Is Written As... If... | as limₙₜₒ∞ aₙ = L // if the terms of the sequence approach a unique number, L, as n increases |
| If The Limit "L" Of A Sequence Exists... | then the sequence converges to L |
| If The Limit "L" Of A Sequence Does Not Exist... | then the sequence diverges |
| A Series Is... | the sum of the numbers in a sequence |
| Sequence Of Partial Sums (Sₙ), Has Terms... | s₁=a₁, s₂=a₁+a₂, ..., sₙ= a₁+a₂+...+aₙ |
| If The Sequence Of Partial Sums (Sₙ) Has A Limit "L", The Infinite Series... | converges to that limit |
| When An Infinite Series Converges, We Can Write... | {∞, ₖ₌₁} ∑aₖ = limₙₜₒ∞ { ₙ, ₖ₌₁} ∑aₖ = limₙₜₒ∞ Sₙ = L |
| Geometric Series | {∞, ₙ₌₀} ∑ar^n = a+ar+ar^2+...+ar^n+... when a≠0 |
| Geometric Series Converges When... | 0<|r|<1 // to the sum "a/1-r" |
| Geometric Series Diverges When... | |r|≥1 |
| nth Term Test Of A Convergent Series | if "{∞, ₙ₌₁} ∑ aₙ" may converge, then limₙₜₒ∞ aₙ = 0 (0 doesn't tell us anything) |
| nth Term Test For Divergence | if limₙₜₒ∞ aₙ ≠ 0, then "{∞, ₙ₌₁} ∑ aₙ" diverges |
| Summary Of The nth Term Test | if the limit is anything other than 0, it diverges // 0 means it May converge, but is inconclusive |
| The Integral Test | if the function meets the requirements, then "{∞, ₙ₌₁} ∑ aₙ" and "{∞, ₁} ∫ f(x)dx" either both converge or diverge |
| Requirements For The Integral Test | positive, continuous, ultimately decreasing, x ≥ a positive integer greater than or equal to 1, aₙ=f(x) |
| The Integral Test Resulting In 0 Is Considered... | inconclusive |
| Steps Of The Integral Test | check for requirements, solve for the integral, if the limit exists both functions converge & if it does not then both functions diverge |
| p-Series | {∞, ₙ₌₁} ∑ 1/(n^p) // when p is a positive number |
| p-Series Converges When... | p>1 |
| p-Series Diverges When... | 0<p≤1 |
| Harmonic Series | {∞, ₙ₌₁} ∑ 1/n = (1/1) + (1/2) + (1/2) + ... + 1/n + ... |
| Harmonic Series Always... | diverges (p=1) |
| Direct Comparison Test | let 0<aₙ≤bₙ // compare aₙ to a function that can solve for convergence and divergence |
| "{∞, ₙ₌₁} ∑aₙ" Converges When... | {∞, ₙ₌₁} ∑bₙ converges (remember: bₙ ≥ aₙ) |
| "{∞, ₙ₌₁} ∑bₙ" Diverges When... | "{∞, ₙ₌₁} ∑aₙ" diverges (remember: bₙ ≥ aₙ) |
| Limit Comparison Test | aₙ>0, bₙ>0, and limₙₜₒ∞(aₙ/bₙ) = L // series ∑aₙ and ∑bₙ both converge or diverge |
Created by:
abievans
Popular Math sets