Hint for Section 4.2 Question 2b

2b)

Let P(n) be the claim: n

     1    

j (j + 1)

=

    n   

n + 1
for all integers ngeq.jpg (602 bytes)1.
S
j = 1
P(1) is the statement: 1

     1      

j (j + 1)

=

   1  

1 + 1
S
j = 1
P(k) is the statement: k

     1     

j (j + 1)

=

    k    

k + 1
S
i = 1
P(k+1) is the statement: k + 1

     1     

j (j + 1)

=

  k + 1 

k + 2
S
i = 1

For a proof by induction, you first need to check that the statement P(1) is true. Then assume that P(k) is true and use this to show that P(k + 1) is true.

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