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| rev | Admin | (Created page with "'''Solution: B''' For the first perpetuity, <math display = "block"> \begin{align*} 32 &=10\left( v^{3}+ v^{6}+\cdot\cdot\cdot\right)=10 v^{3}/\left(1- v^{3}\right)\\ 32-32 v^{3} &=10 v^{3} \\ v^{3} &=32/42. \end{align*} </math> For the second perpetuity <math display = "block"> X= v^{13}+ v^{23}+\cdots= v^{1/3}\,/\,(1- v^{1/3})=(32\,/\,42)^{1/9}\,/\,[1-(32\,/\,42)^{1/9}\,]=32.599. </math> {{soacopyright | 2023 }}") | Nov 18'23 at 8:54 | +424 |