Calculus Examples

$\sum_{n = 1}^{8} \frac{\sin (2^{n} π x)}{2^{n}}$

Step 1

Expand the series for each value of $n$ .

$\frac{\sin (2^{1} π x)}{2^{1}} + \frac{\sin (2^{2} π x)}{2^{2}} + \frac{\sin (2^{3} π x)}{2^{3}} + \dots + \frac{\sin (2^{8} π x)}{2^{8}}$

Step 2

Simplify the expanded form.

$\frac{\sin (2 π x)}{2} + \frac{\sin (4 π x)}{4} + \frac{\sin (8 π x)}{8} + \frac{\sin (16 π x)}{16} + \frac{\sin (32 π x)}{32} + \frac{\sin (64 π x)}{64} + \frac{\sin (128 π x)}{128} + \frac{\sin (256 π x)}{256}$