(In reply to
Puzzle Answer by K Sengupta)
The given expression is equal to:
{1^99+2^99+3^99+........+48^99+49^99} +50^99+
{(100-49)^99+(100-48)^99+.........+(100-3)^99+(100-2)^99+(100-1)^99}
Reducing the terms and rearranging them mod 100, we have:
[{1^99+(-1)^99}+{2^99+(-2)^99}+{3^99+(-3)^99}+...........+{48^99+(-48)^99}
+{49^99+(-49)^99} +50^99] (mod 100)
== 50^99 (mod 100)
==2500 * 50^97 (mod 100)
== 0(mod 100)
Accordingly, the last two digits of the given expression is 00
Consequently, the last digit of the given expression is 0
Edited on September 7, 2022, 2:59 am
Explanation to Puzzle Answer
