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Saturday, June 10, 2006

Sequences and Series

I guess blogger works right now and im hopping that im not going to lose this work. I should have known that saving thing. Anyways here is what we did Wed. Morning:
A superball is dropped from a height of 160 feet. It bounces to (3/5) of its height after it hits the ground. What is the total vertical distance it has traveled when:
a) it hits the ground for the 4th time?





















As you can see that this question have 3 ways to answer.
b) It comes to a rest?

















And there is 3 ways to answer this question too.
Soo is the infinite sum of the series
t1 is the first term
r is the common ratio.
And that was all we did in the morning and this what we did in the afternoon:





















And that was all we did in the afternoon. Oh we did notes on the morning too. Here they are:
Common Ratio (r): I) the number that is repeatedly multiplied to successive terms in a geometric sequence.
ii) from the implicit definition (r) is the base of the exponential function.
To find the nth term in a geometric sequence
tn=t1r^(n-1)
tn is the nth term
n is the rank of the nth term
t1 is the first term
r is the common ratio
Sigma notation: A shorthand way to write a series.
Oh and there is one thing before I finish. The smallest number a calculator can get to is 9.999999999999999*10^(-99)
And the largest number a calculator can get to is 9.999999999999999*10^(99).
Example:
(3/5)^4=.1296
(3/5)^41=8.02*10^(-10)
(3/5)^100=6.53*10^(-23)
(3/5)^1000=0 (its not really 0 but the calculator shows 0 because this number is really small, smaller than that number that's why the calculator shows 0.)
Oh and Thales thought magnets had souls.
anyways that is all for my scribe, you guys have fun.



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