Asked by Cons
How many blocks are needed to build a stair step pattern that has a base of 10, a height of 10, and where each step is one block high and one block deep?
Answers
Answered by
Steve
looks like you just want the sum of all the numbers from 1 to 10.
If you list the numbers, you get
1 2 3 4 ... 8 9 10
Now pair them up, starting from the ends. Each pair adds up to 11. There are 10 numbers, so 5 pairs, adding up to 11*5 = 55
Since it looks like you are going to come up against this again, note that if you add up the first n numbers, the sum is
n(n+1)/2
If you list the numbers, you get
1 2 3 4 ... 8 9 10
Now pair them up, starting from the ends. Each pair adds up to 11. There are 10 numbers, so 5 pairs, adding up to 11*5 = 55
Since it looks like you are going to come up against this again, note that if you add up the first n numbers, the sum is
n(n+1)/2
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