Question
Find the exact value of the expression by identifying it as a known series.$$1+0.2+\frac{0.2^{2}}{2 !}+\frac{0.2^{3}}{3 !}+\frac{0.2^{4}}{4 !}+\cdots$$
Step 1
The series given is: $$1+0.2+\frac{0.2^{2}}{2 !}+\frac{0.2^{3}}{3 !}+\frac{0.2^{4}}{4 !}+\cdots$$ This series can be rewritten as: $$1+x+\frac{x^{2}}{2 !}+\frac{x^{3}}{3 !}+\frac{x^{4}}{4 !}+\cdots$$ where $x = 0.2$. Show more…
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