Question 18

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Jambmaths question: 

Evaluate $\tfrac{1}{2}-\tfrac{1}{4}+\tfrac{1}{8}-\tfrac{1}{16}+---$

Option A: 

$\tfrac{2}{3}$

Option B: 

0

Option C: 

$-\tfrac{2}{3}$

Option D: 

$-1$

Jamb Maths Solution: 

$\begin{align}  & a=\tfrac{1}{2} \\ & r=\frac{-\tfrac{1}{4}}{\tfrac{1}{2}}=-\tfrac{1}{2} \\ & {{S}_{\infty }}=\frac{a}{1-r}=\frac{\tfrac{1}{2}}{1-(-\tfrac{1}{2})}=\frac{\tfrac{1}{2}}{1+\tfrac{1}{2}}=\frac{\tfrac{1}{2}}{\tfrac{3}{2}}=\frac{1}{3} \\\end{align}$

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