+0  
 
0
106
2
avatar

Find the units digits of \(1 + 9 + 9^2 + 9^3 + \dots + 9^{100}\)

 Jul 6, 2020
 #1
avatar
0

sumfor(n, 0, 100, 9^n) =2.988157375 E+95 - This number ends in 501

 Jul 6, 2020
 #2
avatar+31340 
+1

Every even power of 9 ends in 1, every odd power ends in 9.  There are 51 even powers (including 90) and 50 odd powers.

 

Summing these we get 51*1 + 50*9 = 501, so the sum ends in 1.

 Jul 6, 2020

29 Online Users

avatar
avatar
avatar