If the geometric series has first term and common ratio , then its -th partial sum is
Multiply both sides by , then subtract from to eliminate all the middle terms and solve for :
The -th partial sum for the series of reciprocal terms (denoted by ) can be computed similarly:
We're given that , and the sum of the first terms of the series is
and the sum of their reciprocals is
By substitution,
Manipulating the equation gives
so that substituting again yields
and it follows that
What kind of math problems?
Answer:
B-1
Step-by-step explanation:
You can draw a vertical line of symmetry in the middle of the figure. This would be one line.
Answer:
Red: y=(x+6)^2-1
Blue: y=-(x+3)^2+1
Green: y=(x^2-1)
Orange: y=-(x-3)^2+1
Purple: y=(x-6)^2-1
Step-by-step explanation:
Use Desmos to check