8.4. Taylor Series

Example 8.4.18 (d): Finding Taylor Series by Integration

Start with a known series and integrate both sides.


Which function is represented by the series 1/n xn

Our known series with which to start is, once again, the Geometric series. For variety, let's use t as variable:

1/1-t = tn = tn-1

Integrating both sides gives:

1/1-t dt = tn-1 dt = tn-1 dt = 1/n xn

Thus, the function represented by this series is:

1/n xn = 1/1-t dt = -ln(1-x)
1/n xn f(x) = -ln(1-x)
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