## Unit 07: Mathmatical Induction and Binomial Theorem (Solutions)

This is a seventh unit of the book Mathematics 11 published by Khyber Pakhtunkhwa Textbook Board, Peshawar, Pakistan. On this page we have provided the solutions of the questions.

After reading this unit the students will be able to

- Describe the principle of mathematical induction.
- Apply the principle to prove the statements, identities or formulae.
- Use Pascal's triangle to find the expansion of $(x+y)^n$ where $n$ is a small positive integer.
- State and prove binomial theorem for positive integral index.
- Expand $(x+y)^n$ using binomial theorem and find its general term.
- Find the specified term in the expansion of $(x+ y)^n.$
- Expand $(1 +x)^n$ where $n$ is a positive integer and extend this result for all rational values of $n.$
- Expand $(l +x)^n$ in ascending powers of $x$ and explain its validity/convergence for $|x| < 1$ where $n$ is a rational number.
- Determine the approximate values of the binomial expansions having indices as -ve integers or fractions.