Mathematical Induction is a special technique used to prove a given statement about any wellordered set n of natural numbers or we can say if a statement is true for n=1 and n=n than it always true for n=n+1. Mathematical Induction is a magic trick for defining additive, subtracting, multiplication and division properties of natural numbers. Directly, every year you will get 1  2 questions in JEE Main exam as well as in other engineering entrance exams. Indirectly, the concept of Mathematical Induction is widely used in many topics like Sequence and Series, Binomial Theorem, Trigonometry, etc.
This chapter checks your observing power, mathematical reasoning, and creativity towards the problem. In simple words, if you are preparing for JEE Mains or other engineering exams this chapter helps you to increase your calculative approach as well as thinking ability. As you start doing problems on mathematical induction definitely your attitude becomes change toward mathematics.
Let us discuss your present situation,
If you are selected in a good college it proofs that you worked hard during their studies and vice versa. Here the second statement proofs their previous statement.
Let's take another example
Suppose that bicycles are parked in series and you pushed a cycle over another cycle what happened?
The first bicycle falls on adjacent cycle and this will continue till the last cycle will fall
Why this is happening have you ever think?
The reason comes from Mathematical Induction.
Now Solve some previous JEE Mains examples using Mathematical Induction:
From Trigonometry,
Let
on rationalizing,
Now if you put A=30º in the options you can easily find that option (b) is satisfied.
Now, you can check the given by using different angles but be careful with the values which you are choosing and check the solution at least for two values.
Similarly, In Sequence and Series,
We can consider any A.P. series like 1,3,5...... (where a=1, d=2)
G.P. series like 1,3,9.......(a=1, r=3)
H.P. series like
The Principle of Mathematical Induction
The Principle of Mathematical Induction is defined as if a statement S(n) involving n natural number is true for n=1 and if S(n) is true for n=k (where k is any positive integer ) and it also proves that it is true for n=k+1 than S(n) is always true for natural numbers n.
Follow these tips to prepare the chapter Mathematical Induction.
First, finish all the concepts, example and questions given in NCERT Maths Book. You must thorough with the theory of NCERT. Then you can refer to the book Cengage Mathematics Algebra. Mathematical Induction is explained very well in this book and there are ample amount of questions with crystal clear concepts. You can also refer to the book Arihant Algebra by SK Goyal or RD Sharma. But again the choice of reference book depends on person to person, find the book that best suits you the best depending on how well you are clear with the concepts and the difficulty of the questions you require.
Chapters 
Chapters Name 
Chapter 1 

Chapter 2 

Chapter 3 

Chapter 4 

Chapter 5 

Chapter 6 

Chapter 7 

Chapter 8 

Chapter 9 

Chapter 10 

Chapter 11 

Chapter 12 

Chapter 13 

Chapter 14 

Chapter 15 
Directions : Question is AssertionReason type. This question contains two statements :
Statement1 (Assertion) and Statement2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice .
Statement1: For every natural number
Statement2: For every natural number .
Statement1 is true, Statement2 is false
Statemen1 is false, Statement2 is true
Statement1 is true, Statement2 is true Statement 2 is a correct explanation for Statement1
Statement1 is true, Statement2 is true Statement 2 is not a correct explanation for Statement1
Let . Then which of the following is true?
is correct
principle of mathematical induction can be used to prove the formula
If having radical signs then by methods of mathematical induction which is true