Question

find the unit digit of the number( 1^17+3^17+5^17+7^17+9^17+11^17+13^17+..........+49^17)

Answer 1

•unit digit in 1^17 is one
•unit digit in 3^17 is 3
as 3^0=1
3^1=3
3^2=9
3^3=27
3^4=81
•AGAIN AFTER POWER 4 THIS REPEATS
THUS AFTER POWER 16
3 REPEATS AGAIN
•unit digit in 5^x=5
•same as unit digit 9^17 = 9
then this repeats again
unit digit in 11^17=1
and so on
thus for unit digit
(1+3+5+9)*5
if we multiply any natural number with 5 we get the unit digit 5
thus unit digit comes out 5