- Easier to tell if a series converges than what it converges to
- Limit is often approximated
- Section 10.6
- Definition: sum of (-1)n+1 un = u1 - u2 + u3 - u4 + ...
- Example: alternating harmonic series
- Sum of (-1)n (1/n) converges, unlike regular harmonic series
- Alternating series converges if
- All u’s positive
- u’s are non-increasing
- un approaches 0 as n approaches ∞
- Conditional convergence
- Converges, but not absolutely
- i.e., sum of |an| does not converge
- Simple rules for estimating error in finite sum approximations
- Examples
- Sum from 2 of (-1)n ( 1 / ln(n2) )
- Sum from 1 of (-1)n (1/3)n = L
- Give range of possible L values based on s2
- Calculate L exactly
- Sum of (-2)n
- Limit of un = limit of 2n is infinite, fails alternating series (and nth term) test
- Sum from 2 of (-1)n ( 1 / ln(n2) )
- Power Series
- Definition: sum of cn(?)? ...
- Read section 10.7 (“Power Series”)