NCERT Class 11 Mathematics Solutions: Chapter 8 –Binomial Theorem Miscellaneous Exercise Part 3
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Binomials Expressions
1. Find the coefficient of in the product using binomial theorem.
Answer:
Using Binomial Theorem, the expressions, , can be expanded as
The complete multiplication of the two brackets is not required to be carried out.
Only those terms, which involve , are required.
The terms containing are
The coefficient of in the given product is .
2. If are distinct integers, prove that is a factor of , whenever is a positive integer. [Hint: write and expand]
Answer:
In order to prove that ) is a factor of , it has to be proved that , where is some natural number
It can be written that
Where, is a natural number.
This shows that is a factor of , where n is a positive integer.