Solve the problem.
-England decides to decrease its taxes by £7 billion. It is estimated that of each pound received, a typical citizen will spend 90%. The level of economic activity generated by the tax cut is therefore estimated to be: $7 \cdot ( 0.90 ) + 7 \cdot ( 0.90 ) ^ { 2 } + 7 \cdot ( 0.90 ) ^ { 3 } + \ldots$ billion pounds. This amount is equal to what?
A) £63 billion
B) £70 billion
C) £3.6 billion
D) £45 billion
E) none of these

Question

Quizplus · Accepted Answer

The given series is a geometric series with the first term $a = 7$ (billion pounds) and common ratio $r = 0.90$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$. Substituting the given values, we get $S = \frac{7}{1 - 0.90} = \frac{7}{0.10} = 70$ billion pounds. However, the correct mathematical calculation leads to £70 billion, which is not an option listed correctly according to the calculation. Given the options, the closest or intended correct answer might have been misstated, suggesting a potential error in the options provided or in the interpretation of the question.

Solve the Problem 7⋅(0.90)+7⋅(0.90)2+7⋅(0.90)3+…7 \cdot ( 0.90 ) + 7 \cdot ( 0.90 ) ^ { 2 } + 7 \cdot ( 0.90 ) ^ { 3 } + \ldots7⋅(0.90)+7⋅(0.90)2+7⋅(0.90)3+…

Solve the Problem $7 \cdot ( 0.90 ) + 7 \cdot ( 0.90 ) ^ { 2 } + 7 \cdot ( 0.90 ) ^ { 3 } + \ldots$