All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)

(ii)

As

(iii)

Let P(n) be the statement “” for

When .

Thus, P(1) is true.

Assume P(k) is true for some , i.e.

To prove P(k+1) is true, i.e.

Since P(1) is true, by Mathematical Induction, P(k) is true P(k+1) is true, P(n) is true for all

### KS Comments:

This question is quite straight forward. Some students did not realise to use the given recurrence relation to solve the MI.