Problem 477

Diana received 65 points on a project for school. She can make changes and receive three-tenths of the missing points back. She can make as many corrections as she wants. Create the formula for the sum of this geometric series, and explain your steps in solving for the maximum grade Diana can receive. Identify this as converging or diverging.




Diana received 65 points,
let maximum points were 100, so remaining points are 35,
after a correction she gets 35(\frac{3}{10}) points back,
so total points back = 35(\frac{3}{10})+35(\frac{3}{10})^{2}+35(\frac{3}{10})^{3}
point back = summation 35(\frac{3}{10})^{i}  , where i = 1 to infinite
so sum for infinite series S = \frac{a}{1-r}
S = \frac{(35(\frac{3}{10}))}{1-\frac{3}{10}}
S = \frac{ (\frac{105}{10})}{\frac{7}{10}}
S = 15

So maximum grade Diana can receive = 65 +15 = 80

this is converging a r is in range of (0,1)


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