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The governmet injects 90 billion dollars into the economy. Each recipient spends 90% of the dollars received. In turn, the secondary recipients spend 90% of the dollars they recieve. etc. Use the expansion of 1/(1-x) in powers of x to come up with a clean measurement of the total spending that results from the 90 billion dollars injection.
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So if we assume (not true, but not a gross assumption) that the money keeps turning over, the effect is \[9(10^{10})\sum_{k=1}^{∞}(9/10)k=9(10^{10})(1/(1−0.9)−1)=8.1(10^{11})\]
The 90 billion subtracted as the last term is due to the fact that our formula sums from zero, and in this case, we only summed from one.
Detected another typo..... terms summed should be (9/10)^k.
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