Question Number 96318 by M±th+et+s last updated on 31/May/20
$${if} \\ $$$$\left(\mathrm{1}+{x}\right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right).....\left(\mathrm{1}+{x}^{\mathrm{128}} \right)=\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}{x}^{{r}} \\ $$$${then}\:{find}\:{n} \\ $$
Commented by mr W last updated on 31/May/20
$${n}=\mathrm{1}+\mathrm{2}+\mathrm{3}+...+\mathrm{128}=\frac{\mathrm{128}×\mathrm{129}}{\mathrm{2}}=\mathrm{8256} \\ $$
Commented by M±th+et+s last updated on 31/May/20
$${thanks}\:{sir} \\ $$
Commented by mr W last updated on 31/May/20
$${but} \\ $$$$\left(\mathrm{1}+{x}\right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right).....\left(\mathrm{1}+{x}^{\mathrm{128}} \right)=\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}{a}_{{r}} {x}^{{r}} \neq\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}{x}^{{r}} \\ $$
Commented by M±th+et+s last updated on 31/May/20
$${yes}\:{sorry}\:{its}\:\left(\mathrm{1}+{x}\right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{\mathrm{4}} \right)....\left(\mathrm{1}+{x}^{\mathrm{128}} \right) \\ $$