First Principle of Mathematical Induction

$1^2+2^2+3^2+...+n^2=?$,  $\forall n\in \mathrm{N}$.

Elaborate the differences between Deductive and Inductive Reasoning?

State whether the following statement is true or false.

There are no positive integers strictly between $0 \& 1$. 

State whether the following statement is true or false.

The well-ordering principle is a property of the positive integers which is equivalent to the statement of the principle of mathematical induction.

Generalisation step is proved using

Which step concludes or proves the given statement 

A statement $P\left(n\right)$ is true, where $n$ is a natural number.

The assumption in the inductive step is called as inductive hypothesis is

A statement $P\left(n\right)$ is true, where $n$ is a natural number. Then

Consider a statement $P\left(n\right)$, where $n$ is a positive integers. Then in the verification step

Consider a statement $P\left(n\right)$, where $n$ is a natural number. Then in the verification step

$\frac{1}{n+1}+\frac{1}{n+2}+.\dots ..+\frac{1}{2n}>\frac{13}{24}$ is true for all $$

For every natural number $n, P\left(n\right)=n\left(n+1\right)$ is always

Identify the incorrect statement

Which of the following is not true?

James Cameron’s last three movies were successful. His next movie will be successful.

Identify the reasoning process.

I got up at nine o’clock for the past week. I will get up at nine o’clock tomorrow.

For every natural number $k$, which of the following is true?

$P\left(n\right)=n\left(n+1\right)\left(n+5\right), n\in N$ is a multiple of

Using principle of mathematical induction that, prove that $a^{2n}-b^{2n}$ is divisible by $a+b$.

Prove by the principle of mathematical induction that $\left(2n+7\right)<{\left(n+3\right)}^2$ for all $n\in N$.