Problem 29 of 7
Derive the finite geometric series formula for S=3+3r+3r^2+.+3r^(n-1) by subtracting a shifted series.
Using a hint is okay. It just tells the trainer to give you a little more review.
Hidden until you reveal it.
multiply by r, subtract, and solve for sum.
Hidden until you reveal it.
Multiply by r, subtract, and solve for the sum.
Enter your answer
Your answer is equivalent to the expected form.
Walkthrough
Full solution stays hidden until you ask for it.
1. Write S as the finite sum.
2. Write rS as the shifted finite sum.
3. Subtract to cancel the middle terms.
4. Solve for S and state the r!=1 condition.
Use the worked steps, then substitute the final answer back into the original relationship to confirm it satisfies the prompt.
Memorized formula statements with no shifted-series subtraction when derivation is requested.