Please write the code below in LaTeX code up to the lines, Then answer the proof
ID: 3534223 • Letter: P
Question
Please write the code below in LaTeX code up to the lines, Then answer the proof in to the Theorem in LaTex... Will rate well, Thank you :)
Ralph Kelsey
Ohio University
2013 Spring Semester
April, 15, 2013.
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Notes: The title should be in approximately twice the type size as the other lines. Use your name, and the correct due date.
5.2. The second page is the statement and proof of the following theorem:
Theorem. For integer , (n(n+1))/2
Proof: ...
Explanation / Answer
The number e is an important mathematical constant, approximately equal to 2.71828, that is the base of the natural logarithm.[1] It is the limit of (1 + 1/n)n as n approaches infinity, an expression that arises in the study of compound interest, and can also be calculated as the sum of the infinite series[2]
The constant can be defined in many ways; for example, e is the unique real number such that the value of the derivative (slope of the tangent line) of the function f(x) = ex at the point x = 0 is equal to 1.[3] The function ex so defined is called the exponential function, and its inverse is the natural logarithm, or logarithm to base e. The natural logarithm of a positive number k can also be defined directly as the area under the curve y = 1/x between x = 1 and x = k, in which case, e is the number whose natural logarithm is 1. There are also more alternative characterizations.
Sometimes called Euler's number after the Swiss mathematician Leonhard Euler, e is not to be confused with ?