Mathematics

Problem

Consider the following infinite series.

S_{1}=\displaystyle \sum_{n=0}^{\infty} 4(0.5)^{n}

S_{2}=\displaystyle \sum_{n=0}^{\infty} 5(0.4)^{n}

S_{3}=\displaystyle \sum_{n=0}^{\infty} 6(0.3)^{n}

Which of the following correctly orders the sums

S_{1},\,S_{2},\,S_{3}

from least to greatest? a)

S_{3} < S_{2} < S_{1}

S_{1} < S_{3} < S_{2}

S_{1} < S_{2} < S_{3}

S_{2} < S_{1} < S_{3}