A root of x2 – 5x – 1 = 0 is
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I don't know if there was supposed to be an image or something attached, but anything greater than 5,043 would be represented in the inequality
.
This includes every number greater than 5,043, including 5,044, 1,000,000, and everything in between and above.
I'm guessing S^20 is actually referring to the 20th partial sum 
, with
in the arithmetic case, and
in the geometric case.
(a) Combining like terms, we have
and invoking the formula
we end up with
(b) Multiply by 1.1, then subtract this from :
in the arithmetic case, and
in the geometric case.
(a) Combining like terms, we have
and invoking the formula
we end up with
(b) Multiply
To get a sum of 3, you must roll a 1 and a 2. To get a sum of 8, you must roll a 5 and 3, or two 4's.
There are two ways of rolling a 1 and a 2, two ways of rolling a 5 and a 3, and one way to roll two 4's.
There are
possible outcomes when rolling two such solids.
So the probability of getting a sum of 3 or 8 is
There are two ways of rolling a 1 and a 2, two ways of rolling a 5 and a 3, and one way to roll two 4's.
There are
So the probability of getting a sum of 3 or 8 is