=\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-...-\frac{1}{97}+\frac{1}{97}+\frac{1}{100}=1-\frac{1}{100}=\frac{99}{100}
=
$\frac{1}{1}
$-
$\frac{1}{4}
$+
$\frac{1}{4}
$-
$\frac{1}{7}
$+
$\frac{1}{7}
$-...-
$\frac{1}{97}
$+
$\frac{1}{97}
$+
$\frac{1}{100}
$=1-
$\frac{1}{100}
$=
$\frac{99}{100}
$