The difference of the reciprocals of two successive integers equals the product of their reciprocals

see below

Step-by-step explanation:

1         1

--- -

n       n+1

Get a common denominator

1(n+1)          1(n)

-

n(n+1)       (n+1)n

n+1 - n

n(n+1)      

1

n(n+1)

Separate into two fractions

1        1

*

n       n+1

first, you divide the triangle in two, tô form a retangle triangle. after, using pythagoream theorem:

18^2 = 14^2 + (x/2)^2

(x^2/4) + 196 = 324

x^2/4 = 324 - 196

x^2/4 = 128

x^2 = 512

x = √512

x = √2^9

x = 16√2 cm

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step-by-step explanation: