AP Calculus BC / Unit 10: Infinite Sequences and Series
10.1 Defining Convergent and Divergent Infinite Series
Notes
An infinite series $\displaystyle \sum a_n$ converges if its partial sums $S_n=a_1+\dots+a_n$ approach a finite number. Otherwise it diverges.
Practice
The partial sums of a series are $\displaystyle S_n=3-\frac{1}{n}$. The series:
$\displaystyle \lim S_n=3$.
A series whose partial sums are $1, 0, 1, 0, \dots$:
The partial sums don't settle.
A series converges when:
That's the definition.
Ready for more? Take the Unit 10 test.