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Question Number 139104 by I want to learn more last updated on 22/Apr/21

$$\mathrm{Make}\mathrm{r}\mathrm{subject}\mathrm{formula}:{\mathrm{S}}_{\mathrm{n}}=\frac{\mathrm{a}(1-{\mathrm{r}}^{\mathrm{n}})}{1-\mathrm{r}}$$

Commented by mr W last updated on 22/Apr/21

$$you{can}^{\prime }t!thereisnoformulafor$$$$therootsof{n}^{th}degreepolynomial$$$$equation.$$

Commented by I want to learn more last updated on 22/Apr/21

$$\mathrm{Thanks}\mathrm{sir},\mathrm{i}\mathrm{appreciate}$$

Commented by I want to learn more last updated on 23/Apr/21

$$\mathrm{Can}\mathrm{we}\mathrm{find}\mathrm{r}\mathrm{here}?{\mathrm{r}}^{\mathrm{n}}=\mathrm{r}\theta +\beta$$

Commented by MJS_new last updated on 23/Apr/21

$$\mathrm{no}.$$$${\mathrm{r}}^n+pr+q=0$$$$\mathrm{is}\mathrm{solveable}\mathrm{for}n\in \mathbb{Z}\wedge -4⩽n⩽4\mathrm{but}\mathrm{not}\mathrm{generally}$$

Answered by MJS_new last updated on 22/Apr/21

$$\frac{S_n}{a}=\frac{(1-r)(1+r+r^2+...+r^{n-1})}{1-r}$$$$r^{n-1}+r^{n-2}+...r^1+1-\frac{S_n}{a}=0$$$$\mathrm{further}\mathrm{steps}\mathrm{impossible}$$

Commented by I want to learn more last updated on 23/Apr/21

$$\mathrm{Thanks}\mathrm{sir}.$$

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