Question 1: Using binomial theorem, write down the expansions of the following:
Answer:
… … … i)
Now we calculate the following:
Substituting in i) we get
Question 2: Evaluate the following:
Answer:
Question 3: Find . Hence, evaluate .
Answer:
Now we see, and
In
Question 4: Find . Hence, evaluate
Answer:
We see,
Question 5: Using binomial theorem evaluate each of the following:
Answer:
Question 6: Using binomial theorem prove that is divisible by , where
Answer:
Hence is divisible by , where
Question 7: Using binomial theorem prove that is divisible by
Answer:
Hence is divisible by
Question 8: If is a positive integer, prove that is divisible by .
Answer:
Hence is divisible by .
Question 9: Using binomial theorem, indicate which is larger or .
Answer:
Therefore is greater than .
Question 10: Using binomial theorem, determine which is smaller or .
Answer:
Therefore is the smaller term.
Question 11: Find the value of correct to decimal places.
Answer:
Hence correct to decimal places is
Question 12: Show that , where is divisible by .
Answer:
Hence , where is divisible by .