1. ## Geometric/Arithmatic Series

a)Using the appropriate formula, calculate:
9
Σ
(2)n5n

n
=1

b) A company is considering sending a team of divers, with all the appropriate equipment, down to a famous German U
boat wreck. It will cost $560 for the first metre,$640 for the second metre, $720 for the third metre, and so on increasing$80 each time. Using the appropriate formula, determine how much it will cost to reach the Uboat, which is at a depth of 85 metres?

c) Given that a wealthy historian is willing to pay the company $1,000,000 for any artefacts collected from the U boat in b), what will be the profit (loss) to the company if they go ahead with the dive? The answers I got were: a) -909090910 b)$333,200
c) \$668,800

Did I go wrong? Thanks

Ibrox

2. Is a?
$\sum_{i=1}^{n}\{(-2)^n 5n\}$

its quite unclear

3. Hello, ibrox!

I assume those tiny numbers are exponents.

Using the appropriate formula, calculate: . $\sum^9_{n=1}(\text{-}2)^n\cdot5^n$

We have: . $\sum^9_{n=1}(\text{-}10)^n$

This is a geometric series with first term $a = \text{-}10$,
. . common ratio $r = \text{-}10$, and $n = 9$ terms.

The sum is: . $S \;=\;a\,\frac{1-r^n}{1-r} \;=\;
(\text{-}10)\,\frac{1-(\text{-}10)^9}{1 - (\text{-}10)} \;=\;(\text{-}10)\,\frac{1-(\text{-}1,\!000,\!000,\!000)}{11}$

. . . . . . . . . . . $= \;(\text{-}10)\,\frac{1,\!000,\!000,\!001}{11} \;=\;(\text{-}10)(90,\!909,\!091) \;=\;\boxed{-909,\!090,\!910}$

4. Yes, that's what I meant...hard to use that program so I had to copy/paste. Thanks guys.