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Some More Examples


Example 1:
Prove by mathematical induction,

Solution:

Let P(k) be true for same k N.

P(k + 1) is true if P(k) is true.
By Mathematical induction P(n) is true for all n N.

Example 2:
Prove 1 + 2 + 3 + .....

Solution:
Let P(n) =1 + 2 + 3 + .....

P(k +1) is true if P(k) is true.
P(n) is true for all n N by mathematical induction.

Example 3:
Prove 102n 1+1 is divisible by 11 (using principle of mathematical induction)

Solution:

P(k + 1) is true if P(k) is true.
P(n) is true for all natural numbers.

Example 4:
Prove is divisible by 8.

Solution:
Let P(n) represent the statement
is divisible by 8.

 

​Example 5:
Prove by Mathematical induction,

Solution:
Let P(n) be the statement,






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