Ex.1 2+22+222+2222+22222=
Ex.2 5+55+555+5555=
Ex.3 1+11+111+…11111111=
Find how many elements are being added. Write from 1 to the number of elements as one number. For Ex.1, there are 5 elements making the number 12345.
Since the repeating digit is 2, multiply 2 times the number we just got to get the answer. For Ex.1, we have 2+22+222+2222+22222 = 2(12345) = 24690.
For Ex.2, the repeating number is 5 so we multiply it times 1234. We have 5+55+555+5555 = 5(1234) = 6170.
For Ex.3, the repeating number is 1 so we multiply it times 12345678. We have 1+11+111+1111=11111+111111+1111111+11111111 = 1(12345678) = 12345678.
This would have little use in mental speed math, but might be useful in some computations.