Answer:
(a)Yes, the formula will hold for a geometric series
Explanation:
Part A
The given formula in (2c) is reproduced below:
[tex]T_n=S_n-S_{n-1}[/tex]
This formula will hold for a geometric series since the sum of n terms is an addition of the next term to the previous sum (sum of n-1 terms).
Part B
Given the geometric series:
[tex]3+6+12+24+\cdots[/tex]
Consider the sums below:
[tex]\begin{gathered} S_3=3+6+12=21 \\ S_4=3+6+12+24=45 \\ T_4=24 \\ S_4-S_3=45-21=24 \\ \implies T_4=S_4-S_3 \end{gathered}[/tex]
Thus, the formula is shown to hold.
