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If e were rational, then e = n/m for some positive integers m, n. So then 1/e = m/n. But the series expansion for 1/e is
1/e = 1 - 1/1! + 1/2! - 1/3! + ...
Call the first n values of this alternating series S(n). How good is this approximation to e? Well, the error is bounded by the next part of the alternating series:
0 < | 1/e - S(n) | = | m/n - S(n)| < 1/(n+1)!
But multiplying through by n!, you can see that
0 < | integer - integer | < 1/(n+1) < 1.
But there is no integer between 0 and 1, so this is a contradiction; e must be irrational.
Consider the unary relational symbols P and L, and the binary relational symbol On, where P(a) and I(a) encode that a is a point and a (straight) line in the 2-dimensional space, r
Example of Fractional Equations: Example: Solve the fractional equation (3x +8)/x +5 =0 Solution: Multiply both sides of the equation by the LCD (x). (x) ((3x
Consider an election with 721 voters. A) If there are 5 candidates, at least x votes are needed to have a plurality of the votes. Find x. B) Suppose that at least 73 votes are n
explain the characteristics of statistics
where does goes take place?
Definition: An equation is considered as function if for any x in the domain of the equation (the domain is the entire x's which can be plugged into the equation) the equation wil
At a bakery the cost of 30 experts is 45$. Write an equation that shows the cost of 45 cookies
Define a complete lattice and give one example. Ans: A lattice (L, ≤) is said to be a complete lattice if, and only if every non-empty subset S of L has a greatest lower bound
how to do multiplication
Solve : 4x2+2x+3=0 Ans) x^2 + (1/2)x = -(3/4) (x+1/4)^2 = 1/16 - 3/4 = -11/16 implies x = (-1+i(11)^(1/2))/4 and its conjugate.
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