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 .