# math!

• Oct 24th 2006, 08:09 AM
cutie4ever
math!
hi hows it going? i hope good but for me not that great cuz I don't get math!!!
I have been like trying to understand this question and it it taken me like one hour and it probably really easy but I am really fustrated!
george entered a function into his calculator andfound the following partail sums
s1=0.0016
s2= 0.0096
s3= 0.0496
s4= 0.2496
s5= 1.2496

determine the genral term of the corresponding sequence

• Oct 24th 2006, 08:20 AM
ThePerfectHacker
Quote:

Originally Posted by cutie4ever
hi hows it going? i hope good but for me not that great cuz I don't get math!!!
I have been like trying to understand this question and it it taken me like one hour and it probably really easy but I am really fustrated!
george entered a function into his calculator andfound the following partail sums
s1=0.0016
s2= 0.0096
s3= 0.0496
s4= 0.2496
s5= 1.2496

$S_1=a_1=.0016$
$S_2=a_1+a_2=.0096\to a_2=.008$
$S_3=a_1+a_2+a_3=.0496\to a_3=.04$
$S_4=a_1+a_2+a_3+a_4=.2496\to a_4=.2$
$S_5=a_1+a_2+a_3+a_4+a_5=1.2496\to a_5=1$
Thus,
$.0016,.008,.04,.2,1$
It seems that this is a geometric series,
Because you have,
16,8,4,2,1....
Powers of two.
• Oct 24th 2006, 01:33 PM
Soroban
Hello, cutie4ever!

Quote:

George entered a function into his calculator and found the following partail sums:

. . $\begin{array}{ccccc}s_1 = 0.0016\\s_2 = 0.0096\\ s_3 = 0.0496 \\ s_4 = 0.2496 \\ s_5 = 1.2496\end{array}$

Determine the general term of the corresponding sequence.

If you covert the decimals to fractions, a pattern emerges.

$\begin{array}{cccccc}s_1 & = & \frac{16}{10,000} \\ s_2 & = & \frac{16}{10,000} + \frac{8}{1000}\\s_3 & = & \left(\frac{16}{10,000} + \frac{8}{1000}\right) + \frac{4}{100}\\s_4 & = & \left(\frac{16}{10,000} + \frac{8}{1000} + \frac{4}{100}\right) + \frac{2}{10}\\ \vdots & & \vdots\end{array}$

Each sum is the preceding sum plus a power of: $\frac{2}{10} = \frac{1}{5} = 5^{-1}$

It begins with: $\frac{16}{10,000} = 5^{-4}$ . and we add: $5^{-3},\;5^{-2},\;5^{-1},\;\hdots$

Hence, the series is: . $s \:=\:5^{-4} + 5^{-3} + 5^{-2} + 5^{-1} + \hdots$

Therefore, the general term is: . $a_n\;=\;5^{n-5}$