Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.5 + 5 ?  + 5 ? 2 + ... + 5 ? n - 1 = 

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First we show that the statement is true when n = 1.
 For n = 1, we get 3 =  = 3.
This is a true statement and Condition I is satisfied.

Next, we assume the statement holds for some k. That is,
  is true for some positive integer k.
We need to show that the statement holds for k + 1. That is, we need to show that
 
So we assume that  is true and add the next term,  to both sides of the equation.
5 + 5 ?  + 5 ? 2 + ... + 5 ? k - 1 + 5 ? (k + 1) - 1 + 5 ? (k + 1) - 1
  + 5k
  + 
 
 
 
Condition II is satisfied. As a result, the statement is true for all natural numbers n.

Mathematics

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A.

B.

C.

D.

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Find the value of the expression. ? 

A.  
B.
C.  
D.  

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Find the difference. Assume that all variable factors in the denominators are not equal to zero. - 

A.  
B. 5
C.  
D.

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Write an equation for the line with an x-intercept of -4 and y-intercept of 16.

What will be an ideal response?

Mathematics