- #1
Lebombo
- 144
- 0
A geometric series is [itex]S_{n}= a_{1} + a_{2} + a_{3} + ...+ a_{n} = a_{1}r^{0} + a_{2}r^{1} + a_{3}r^{2} + ...+ a_{n}r^{n-1}[/itex]
In a geometric series, the first term = [itex]a_{1}[/itex]
The common ratio = [itex]\frac{a_{n+1}}{a_{n}}[/itex]
The nth term of a geometric sequence is [itex]a_{n}= a_{1}r^{n-1}= a_{1}(\frac{a_{n+1}}{a_{n}})^{n-1}[/itex]
The question is:
In the summand of the sigma notation, can the general term of geometric sequence formula be expressed this way:
[tex]S_{n}= \sum_{i=1}^n a_{1}r^{i-1} = \sum_{i=1}^n a_{1}(\frac{a_{i+1}}{a_{i}})^{i-1}[/tex]
In a geometric series, the first term = [itex]a_{1}[/itex]
The common ratio = [itex]\frac{a_{n+1}}{a_{n}}[/itex]
The nth term of a geometric sequence is [itex]a_{n}= a_{1}r^{n-1}= a_{1}(\frac{a_{n+1}}{a_{n}})^{n-1}[/itex]
The question is:
In the summand of the sigma notation, can the general term of geometric sequence formula be expressed this way:
[tex]S_{n}= \sum_{i=1}^n a_{1}r^{i-1} = \sum_{i=1}^n a_{1}(\frac{a_{i+1}}{a_{i}})^{i-1}[/tex]