Given that the geometric series $1+{{\mathrm{e}}^{-x}}+{{\mathrm{e}}^{-2x}}+...$has a sum to infinit

Question

Given that the geometric series $1+{{\mathrm{e}}^{-x}}+{{\mathrm{e}}^{-2x}}+...$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 $S-{{S}_{n}}10\ln 10$.

Accepted Answer

x > 0 (shown); n > 10 ln 10 (shown)

CJC APGP Tutorial Q5

CJC APGP Tutorial Q5

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