Question

Explain why there is no infinite geometric series with first term 10 and sum 4

Answer 1

`\mathrm{The\ sum\ of\ infinite\ series\ is\ given\ by\ the\ formula:}\\S=(a)/(1-r)\\\mathrm{where,\ }-1 \le r \le 1\\\mathrm{Now,\ if\ we\ put\ here\ }S=4\ \mathrm{and\ }a=10,\\\mathrm{4=}(10)/(1-r)\\\mathrm{or,\ }1-r=2.5\\\mathrm{or,\ }r=1-2.5\\\mathrm{or,\ }r=-1.5\\\mathrm{Here\ the\ value\ of\ }r\ \mathrm{is\ not\ between\ -1\ and\ 1\ inclusive.\ Hence\ there\ is\ no}\\ \mathrm{infinite\ geometric\ series.}`