CJC APGP Tutorial Q5
Given that the geometric series $1+{{\text{e}}^{-x}}+{{\text{e}}^{-2x}}+…$has a sum to infinity, show that $x>0$. When $x=10$, write down the expressions for ${{S}_{n}}$, the sum to $n$ terms, and for $S$, the sum to infinity.
For $S-{{S}_{n}}<\frac{S}{{{10}^{100}}}$, show that $n>10\ln 10$.
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