Engaging with Math: A Cambridge Admission Puzzle Unveiled
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Chapter 1: The Allure of Mathematics
One of the unexpected advantages of studying mathematics is that it offers individuals from diverse backgrounds an accessible and enjoyable pastime: solving math challenges! Research indicates that participating in daily intellectual activities can help slow the aging process and enhance overall happiness. I believe my blog serves as an excellent platform for math lovers worldwide to explore and enjoy the beauty of mathematics.
In this instance, we tackle a problem sourced from the TMUA, a test for aspiring computer science students at Cambridge. Here’s a clue: transitioning from 1 to 20204 mirrors the progression from 1 to 2, then 2 to 3, and so forth, all the way to 2024.
Before proceeding, I encourage you to pause, grab a pen and paper, and give this a shot. Once you feel ready, continue reading for the solution!
Section 1.1: Unraveling the Problem
A fundamental characteristic of definite integrals is that they can be partitioned into multiple intervals. Let’s apply this principle to the integral presented in the problem. We will decompose it into r separate integrals.
Can you identify how we can utilize the provided formula?
For a definite integral of f(x) spanning from n to n + 1, the result is n + 1. The initial integral yields 1, the second 2, and so forth. Remarkably, the upper limit of the integral provides exactly what we need!
Notice the highlighted n + 1? Therefore, we can derive the following:
I'm certain you're familiar with the formula for summing the first n integers!
Do you recognize our direction? We’ve transformed our inquiry into a straightforward summation challenge!
There are various methods to simplify the sum, but given that our upper limit is 8, it may be easiest to compute them manually!
Did you make it into Cambridge this time? And there’s our answer! How remarkable!
What was your thought process during this challenge? Share your insights in the comments; I’m eager to hear from you!
Section 1.2: Sharing the Joy of Math
Have you saved and shared this list of top math puzzles on Medium?
Math Puzzles
The best math puzzles on Medium
Algebra, Geometry, Calculus, Number Theory, and more
Share this with your friends!
The first video titled "Can you solve this Cambridge Entrance Exam Question?" explores a challenging math problem that might inspire your solving skills.
The second video, "OXFORD & CAMBRIDGE INTERVIEW MATH PROBLEM | NO CALCULATOR!" presents another intriguing math challenge that tests your analytical abilities.
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Love, Bella