Methods of Induction and Binomial Theorem — Class 11 Maharashtra HSC Mathematics revision notes
A 5-page visual revision sheet for Methods of Induction and Binomial Theorem, written for Class 11 Maharashtra HSC Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
What this Methods of Induction and Binomial Theorem sheet covers
- The four steps of induction
- Illustration: sum of the first n natural numbers
- the statement P(n)
- Proving a summation formula by induction
- Induction on a more elaborate series
- Induction for divisibility
- Induction on a divisibility statement
- Binomial theorem, positive integer index
- for a,bin R, nin N
- with alternating sign
- Expanding a binomial power
- General and middle terms
- the (r+1)th term of (a+b)^n
- n even: one middle term
- n odd: two middle terms
- Finding a specific term
- Finding the middle term
- Binomial series, negative or fractional index
- n not a positive integer, |x|<1
- A fractional-index expansion
- Standard expansions, |x|<1
- (1+x) to the -1
- (1-x) to the -1
- (1+x) to the -2
- (1-x) to the -2
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Methods of Induction and Binomial Theorem the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.