${B}$ = ${1}$ + $3^{1}$ + $3^{2}$ + $3^{3}$+ .... + $3^{2006}$
${3B}$ = ${3}$ . ( ${1}$ + $3^{1}$ + $3^{2}$ + $3^{3}$+ .... + $3^{2006}$ )
${3B}$ = $3^{1}$ + $3^{2}$ + $3^{3}$+ $3^{4}$ .... + $3^{2007}$
${3B-B}$ = ( $3^{1}$ + $3^{2}$ + $3^{3}$+ $3^{4}$ .... + $3^{2007}$ ) - ( ${1}$ + $3^{1}$ + $3^{2}$ + $3^{3}$+ .... + $3^{2006}$ )
${2B}$ = $3^{2007}$ - ${1}$
${B}$ = $\frac{3^{2007} - 1}{2}$
$\text{STUDY WELL !}$