4.x Sequences Series

4 - Sequences and Series

  • Sum to infity: $s_\infty$

4.4 - Arithmetic series

Proof:

$s_n = a; +; a+d;+;a+2d;+;…;+;a+(n-2)d;+;a+(n-1)d$ $s_n = a+(n-1)d;+;a+(n-2)d;+;…;+;a+2d;+;a+d;+;a$ $2s = n[2a+(n-1)d]$ $$ s = \frac{n}{2}[2a+(n-1)d] $$

4.5 - Geometric series