Prove that 7 + 77 + 777 + … + 777 for all n ϵ N

Let P(n) = 7 + 77 + 777 + … + 777……n times……7



Step1:




Step2:





Now, we need to show that P(m+1) is true whenever P(m) is true.


This is a geometric progression with n = m+1


So, P(m+1) = 7 + 77 + 777 + … + 777……(m+1) times……7







Thus, P(m+1) is true.


So, by principle of mathematical induction, P(n) is true for all nϵN.


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