Make-r-subject-formula-S-n-a-1-r-n-1-r-

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

Make r subject formula : S_{n} = \frac{a (1 - r^{n})}{1 - r}

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

y o u {c a n}^{'} t! t h e r e i s n o f o r m u l a f o r

t h e r o o t s o f n^{t h} d e g r e e p o l y n o m i a l

e q u a t i o n .

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

Thanks sir, i appreciate

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

Can we find r here ? r^{n} = r θ + β

Commented by MJS_new last updated on 23/Apr/21

no .

r^{n} + p r + q = 0

is solveable for n \in Z \land - 4 ⩽ n ⩽ 4 but not generally

Answered by MJS_new last updated on 22/Apr/21

\frac{S_{n}}{a} = \frac{(1 - r) (1 + r + r^{2} + \dots + r^{n - 1})}{1 - r}

r^{n - 1} + r^{n - 2} + \dots r^{1} + 1 - \frac{S_{n}}{a} = 0

further steps impossible

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

Thanks sir .