Monday, February 18, 2019
Sunday, February 17, 2019
Integration : A harder Problem
Most of the studenst will fail to solve this particular integration problem. It is trickier but once you hit the right idea, you will be able to solve the integration problem easily.
Saturday, February 16, 2019
Pigeonhole Principle
The numbers 1 to 20 are placed in any order around a circle. Prove that the sum of some 3 consecutive numbers must be at least 32!
This problem uses the alternate form of pigeon hole principle which is as follows:
If the average of n positive numbers is t, then at least one of the numbers is greater than or equal to t. Further, at least one of the numbers is less than or equal to t.
The proof is very simple, assume the contradiction and proceed!
#Solution https://youtu.be/GLQg6cSAbms
This problem uses the alternate form of pigeon hole principle which is as follows:
If the average of n positive numbers is t, then at least one of the numbers is greater than or equal to t. Further, at least one of the numbers is less than or equal to t.
The proof is very simple, assume the contradiction and proceed!
#Solution https://youtu.be/GLQg6cSAbms
Sum of first 'n, natural numbers
A simple way to calculate the sum of first 'n' natural numbers witout the use of calculator. Infact the same procedure is used to calculate the sum of n terms of any A.P series. See it and try to obtain the formula yourself
Inequality
A challenging problem based on the inequality that square of a real number is always greater than equal to zero. Learn the trick and prepare yourself for more challenging problems based on the same ideology.
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