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Mark44 said:I was not able to open the file. Why not just put the problem and your work directly into the form?
Which is a question of base 3, pretty much by definition!eddybob123 said:@Ray a and b are allowed to vary, but they have to be integral.
@Mark I do not know how to use the codes
@HallsofIvy I am pretty sure that the answer does not involve different bases. The expression is merely a subtraction of powers of 2 over powers of 3.
eddybob123 said:However it will get just as complicated as in base ten because of all the powers of 2
The phrase "Expanding Power of 2 over 3" refers to the mathematical process of raising the number 2 to increasingly higher powers, and then dividing each result by 3. This process can be used to find the sum of an infinite geometric series with a starting term of 2 and a common ratio of 1/3.
This process is important because it allows us to find the sum of an infinite geometric series, which can be applied to various real-world problems such as calculating compound interest, population growth, and radioactive decay.
To prove this homework statement, you will need to use mathematical induction. This involves showing that the statement is true for a specific starting point (usually n = 1), and then proving that if it is true for any value k, it is also true for the next value (k+1). This process must be repeated infinitely to prove the statement for all possible values of n.
One tip for solving this type of problem is to start by writing out the first few terms of the series and looking for patterns. This can help you come up with a general formula for the sum. Additionally, it is important to carefully follow the steps of mathematical induction and clearly explain each step in your proof.
Yes, this process can be applied to any number raised to a power and then divided by a different number. The key is to find the common ratio between each term in the series and use that to create a formula for the sum. However, the specific values used in the homework statement may change depending on the numbers involved.