Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2007 / Paper 1 / Section B / 3 / a / ii

The expression in the PDF is $1/a^x-1$, with the subtraction outside the fraction. Using the exponential series with $a^{-x}=e^{-x\ln a}$ givesFor $a>0$, $a\ne 1$, these are the first two nonzero terms. If $a=1$, the function is identically zero, so there are no nonvanishing terms.