LetS = nk=0arkShow that S rS = a arn+1 and hence thatnk=0ark = a arn+11 r (r = 1)(A sum

Chapter 5, Problem 64

(choose chapter or problem)

Let

$S=\sum_{k=0}^{n} a r^{k}$

Show that $S-r S=a-a r^{n+1}$ and hence that

$\sum_{k=0}^{n} a r^{k}=\frac{a-a e^{n+1}}{1-r}(r \neq 1)$

(A sum of this form is called a geometric sum.)

Equation Transcription:

$S=\sum\limits_{k=0}^{n}a{r}^{k}$

$S-rS=a-a{r}^{n+1}$

$\sum\limits_{k=0}^{n}a{r}^{k}=\frac{a-a{e}^{n+1}}{1-r}(r\ne{}1)$

Text Transcription:

S=sum_k=0 ^n ar^k

S-rS=a-ar^n+1

sum_k=0 ^n ar^k =a-ar^n+1 /1-r (r neq 1)

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