Question Number 98320 by pranesh last updated on 13/Jun/20
Answered by bemath last updated on 13/Jun/20
$$\mathrm{s}\:=\:\frac{\mathrm{1}}{\mathrm{1}−\mathrm{y}}+\frac{\mathrm{x}}{\mathrm{1}−\mathrm{y}}+\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{1}−\mathrm{y}}+\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{1}−\mathrm{y}}+ \\ $$$$…\:+\frac{\mathrm{x}^{\mathrm{n}} }{\mathrm{1}−\mathrm{y}}\:+…=\frac{\frac{\mathrm{1}}{\mathrm{1}−\mathrm{x}}}{\mathrm{1}−\mathrm{y}}\: \\ $$$$=\:\frac{\mathrm{1}}{\left(\mathrm{1}−\mathrm{x}\right)\left(\mathrm{1}−\mathrm{y}\right)}\:;\:\mid\mathrm{x}\mid\:<\mathrm{1}\:\&\mid\mathrm{y}\mid<\mathrm{1} \\ $$