Question Number 136331 by mohammad17 last updated on 20/Mar/21
Answered by mr W last updated on 20/Mar/21
$$\mathrm{5}×\mathrm{3}^{{n}+\mathrm{1}} ×\mathrm{2}^{\mathrm{1}−\mathrm{2}{n}} \\ $$$$=\mathrm{5}×\mathrm{3}^{{n}} ×\mathrm{3}×\mathrm{2}×\mathrm{4}^{−{n}} \\ $$$$=\mathrm{30}×\left(\frac{\mathrm{3}}{\mathrm{4}}\overset{{n}} {\right)} \\ $$$$\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\mathrm{30}×\left(\frac{\mathrm{3}}{\mathrm{4}}\overset{{n}} {\right)}=\mathrm{30}×\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{2}} \frac{\mathrm{1}}{\mathrm{1}−\frac{\mathrm{3}}{\mathrm{4}}}=\mathrm{67}.\mathrm{5} \\ $$