Find two consecutive natural numbers

Question

Find two consecutive natural numbers such hat the difference of their reciprocals is 1/7 the reciprocal of the smaller number

Answer 1

Let the 2 consecutive natural numbers be

 

n

n + 1.

 

1/n - 1/(n + 1) = (1/7)(1/n)

 

(6/7)(1/n) = 1/(n + 1)

 

(6/7)(n + 1) = n

 

6n + 6 = 7n

 

n = 6

n + 1 = 7

 

Test the answer.  Is

 

1/6 - 1/7 = (1/7)(1/6) ?

 

1/6 - 1/7 = (7 - 6)/42 = 1/42

(1/7)(1/6) = 1/42  [good]