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- A sentence is called a statement if it can be adjudged as true or false. Every statement is a sentence, but a sentence may or may not be a statement.
- A statement involving natural number n is generally denoted by P(n).
- Principle of mathematical induction states that if P(n) is a statement involving natural number n and
- P(1) is true, i.e., the statement is true for n=1.
- Truth of P(k) implies the truth of P(k+1) i.e., the statement is true for n = k+1 assuming it to be true for n = k, then the statement P(n) is true for all natural numbers.
- A binomial is an algebraic expression of two terms which are connected by the operations '+' or '-'.
- The binomial theorem for natural numbers states that

- Pascal's triangle

- General term
For 0 < r < n, Tr+1 in the expression of (a + b)n is given by Tr+1 = nCran-rbr.
- (r + 1)th term at the end in the expansion of (a+b)n is same as the (r + 1)th term at the beginning in (b+a)n.
- Middle terms
- If n is an odd natural number, then there are two middle terms in the expansion of (a + b)n and are given by 
- i) The sum of all binomial coefficients in the expansion of (1+x)n is 2n.



- The binomial theorem for fractional index states that
- General term
0, Tr+1 in the expansion of (1+x)n, |x|<1,n
Q is given by

- If x be so small that its squares and higher powers may be neglected, then (1+x)n= 1 + nx (approximately).
- If x be so small that its cube and higher powers may be neglected, then


