SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Proof, EXT2 P2 EQ-Bank 8

Prove by mathematical induction that    for integral  .  (3 marks)

Show Answers Only

Show Worked Solution
IMPORTANT: Inequality induction is challenging. Students need to state clearly what they need to prove and then use logic to advance their answer toward the desired result.

 

 

 

 

 
 
 
 
 
 
 

 

Proof, EXT2* P2 2013 HSC 14a

  1. Show that for  .    (1 mark)

  2. Use mathematical induction to prove that for all integers  ,
     
        .   (3 marks)

Show Answer Only
Show Worked Solution

i. 

♦♦ Mean mark 25%.
MARKER’S COMMENT: Student algebra was poor in creating a common denominator and justifying why the final expression is always negative proved challenging.
 
 

 

 

ii. 

 

 

♦♦ Mean mark of 26%.
IMPORTANT: Students have to carefully examine part (i) of this question to provide the information required to prove true for .
 
 
 

  

.