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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 byJDamian 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 byRio 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 byKunal12588 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 byRio Michael last updated on 15/Aug/19

thanks

$${thanks} \\ $$

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