Skip to main content

Challenge 345: Forever Fractions

These fractions could go on and on! What can you work out about them?

(i) Find the value of the expression

(ii) Express 29/12 in the form

where a, b, c and d are positive integers.

(iii) What value does the expression below approach as the calculation is made more and more accurate by including more of the parts represented by “…”?