Mental Calculation: fixed missing “138”

THE GREAT BOOK OF FAST AND MENTAL CALCULATION:

Fixed the missing “138” in the “Seven 7” problem

The challenge was to get all the numbers from 1 to 150 using 7 seven times as well as the necessary arithmetic symbols.
In the Great Book of Fast and Mental Calculation, Dario De Toffoli and Furio Honsell had proposed all the solutions… except one. The 138 had in fact remained unsolved, as far as we know no one had managed to reach it with the conditions posed by the problem.
But now an old friend has succeeded, Silvano Berton, who has made it with the triangular numbers. But after all, if the factorial holds, why shouldn’t the triangular hold?
Don Knuth, computer guru, had for example already proposed to call the n-th triangular numbers “terminals”, indicating them with “n?”)… and Furio Honsell validated the solution.

7? = 28 (the 7th triangular seventh)
(7+7)? = 105 (the 14th triangular) therefore:
7? + (7+7)? + 7 – (7+7)/7 = 28 + 105 +7 -2 = 138