Question

a. do you think your formula in 2c ( Tn=Sn-Sn-1) above will hold for a geometric series b. Motivate your response in A using the geometric series: 3+6+12+24+...

Answer 1

(a)Yes, the formula will hold for a geometric series

Explanation:

Part A

The given formula in (2c) is reproduced below:

`T_n=S_n-S_(n-1)`

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:

`3+6+12+24+\cdots`

Consider the sums below:

`\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}`

Thus, the formula is shown to hold.