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for-a-geometric-series-can-the-sun-to-infinty-use-the-two-formulas-S-a-1-r-r-lt-1-and-S-a-r-1-r-gt-1-please-i-am-getting-confused-on-this-




Question Number 66439 by Rio Michael last updated on 15/Aug/19
for a geometric series.  can the sun to infinty use the two formulas  S_∞ = (a/(1−r))  ∣r∣  <1  and S_∞  = (a/(r−1)) ∣r∣ > 1 ?? please i am getting confused on this.
$${for}\:{a}\:{geometric}\:{series}. \\ $$$${can}\:{the}\:{sun}\:{to}\:{infinty}\:{use}\:{the}\:{two}\:{formulas} \\ $$$${S}_{\infty} =\:\frac{{a}}{\mathrm{1}−{r}}\:\:\mid{r}\mid\:\:<\mathrm{1}\:\:{and}\:{S}_{\infty} \:=\:\frac{{a}}{{r}−\mathrm{1}}\:\mid{r}\mid\:>\:\mathrm{1}\:??\:{please}\:{i}\:{am}\:{getting}\:{confused}\:{on}\:{this}. \\ $$
Commented by JDamian last updated on 15/Aug/19
The sum when  n→∞  and  r>1  is ±∞
$${The}\:{sum}\:{when}\:\:{n}\rightarrow\infty\:\:{and}\:\:{r}>\mathrm{1}\:\:{is}\:\pm\infty \\ $$
Commented by Rio Michael last updated on 15/Aug/19
so it can be used? i mean the second formula
$${so}\:{it}\:{can}\:{be}\:{used}?\:{i}\:{mean}\:{the}\:{second}\:{formula} \\ $$
Commented by Kunal12588 last updated on 15/Aug/19
when the series is converging those formulas  can be used
$${when}\:{the}\:{series}\:{is}\:{converging}\:{those}\:{formulas} \\ $$$${can}\:{be}\:{used} \\ $$
Commented by Rio Michael last updated on 15/Aug/19
thanks
$${thanks} \\ $$

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