+142 a) Show that the sum of 11 consecutive integers is always divisible by 11.
b) Show that the sum of 12 consecutive integers is never divisible by 12.
+4624 a): Label the integers: x−5,x−4,x−3,x−2,x−1,x,x+1,x+2,x+3,x+4,x+5=11x . And, this number is a multiple of 11 , so it is definitely divisible by 11.
Try the second one on your own!
+130466 Thanks, tertre......here's another approach
Let the first integer = x
Let the 11th integer = x + 10
Sum = [ first integer + 11th integer] * number of terms / 2 =
[ x + x + 10 ] * 11 / 2 =
[2x + 10 ] * 11 / 2 =
2 [ x + 5 ] * 11 / 2 =
[ x + 5 ] * 11 which is divisible by 11
