Using only p&p(no calculator), determine the value of:
95+94+93+92+9
I'm going to first rearrange the expression into a very specific format:
9^5 + 9^4 + 9^3 + 9^2 + 9
= (9^4 + 9^3 + 9^2 + 9 + 1)*9
= ((9^3 + 9^2 + 9 + 1)*9 + 1)*9
= (((9^2 + 9 + 1)*9 + 1)*9 + 1)*9
= ((((9 + 1)*9 + 1)*9 + 1)*9 + 1)*9
In this final form I can literally do the arithmetic work left-to-right and get the value.
9+1 = 10
10*9 = 90
90+1 = 91
91*9 = 819
819+1 = 820
820*9 = 7380
7380+1 = 7381
7381*9 = 66249
9^5 + 9^4 + 9^3 + 9^2 + 9 = 66249
Pencil and Paper
