x+(x+1)+(x+2)+(x+3)+(x+4)=5x+10 What does this prove about the sum of these natural numbers?

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Step 1

The sum of the given equation is calculated as follows.


Step 2

The term x is a natural number.

Also, each of the terms xx+1, x+2, x+3 and x+4 are natural numbers.

These are 5 consecutive numbers.

The sum of these natural numbers are given as 5x+10.

Step 3

The value of x may vary by time.

Consider the value of x as 1 and obtain the sum as follows.

Step 4

The sum of any set of consecutive natural numbers can be obtained by the given expression.

If we know the value of x, then the direct substitution of that value in to the expression 5x+10 results the sum.

So, it is easy to conclude that the sum of any set of natural numbers is finite.

Step 5


The sum of any set of consecutive natural numbers is finite.

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