College Algebra 7th Edition

$\sum_{k=1}^{100}(-1)^{k+1}* k* x^{k-1}$
We write the sum in sigma notation: (We notice that the terms have the form $(integer)x^{integer-1}$ with consecutive integers and alternating signs.) $1-2x+3x^{2}-4x^{3}+5x^{4}+ \cdots-100x^{99}=\sum_{k=1}^{100}(-1)^{k+1}* k* x^{k-1}$