Question Number 208508 by Tawa11 last updated on 17/Jun/24
$$\mathrm{Evaluate}\:\mathrm{and}\:\mathrm{leave}\:\mathrm{your}\:\mathrm{answer}\:\mathrm{in}\:\mathrm{exponent}\:\mathrm{form}. \\ $$$$\mathrm{5}^{\mathrm{2024}} \:−\:\:\mathrm{5}^{\mathrm{2023}} \:\:−\:\:\mathrm{5}^{\mathrm{2022}} \:\:−\:\:\mathrm{5}^{\mathrm{2021}} \:\:−\:\:\mathrm{5}^{\mathrm{2020}} \:\:−\:\:\mathrm{5}^{\mathrm{2019}} \:\:=\:\:? \\ $$
Answered by mr W last updated on 17/Jun/24
$$=\left(\mathrm{5}^{\mathrm{5}} −\mathrm{5}^{\mathrm{4}} −\mathrm{5}^{\mathrm{3}} −\mathrm{5}^{\mathrm{2}} −\mathrm{5}−\mathrm{1}\right)×\mathrm{5}^{\mathrm{2019}} \\ $$$$=\left(\mathrm{5}^{\mathrm{5}} −\frac{\mathrm{5}^{\mathrm{5}} −\mathrm{1}}{\mathrm{5}−\mathrm{1}}\right)×\mathrm{5}^{\mathrm{2019}} \\ $$$$=\left(\frac{\mathrm{3}×\mathrm{5}^{\mathrm{5}} +\mathrm{1}}{\mathrm{4}}\right)×\mathrm{5}^{\mathrm{2019}} \\ $$$$=\mathrm{2344}×\mathrm{5}^{\mathrm{2019}} \\ $$
Commented by Tawa11 last updated on 17/Jun/24
$$\mathrm{Thanks}\:\mathrm{sir}. \\ $$$$\mathrm{I}\:\mathrm{appreciate}. \\ $$