By the definition above,
and by substitution we get
If we keep following this procedure, we'll start to see a pattern:
and so on, down to
Now,
One of these series is geometric and has a well-known closed form:
The other (see note below) is a bit less obvious, but can be derived:
so we have
# # #
A brief note on how to compute the sum,
The first term of the sum is 0:
Add and substract 1 to the first factor in the summand and expand the sum into two sums:
The latter sum we're familiar with. For the other sum, we can shift the index to make it start at , and again the first term in the sum would be 0:
So we have
Continuing in this way, we would end up getting
or as a double sum,
which is easy to reduce:
X + y + 3 = 0
hope this helps!!!^_~!!!
Answer:
there is a cluster from 1-4
there is a gap from 5-7
The spread is from 1-8
Step-by-step explanation:
These are all true if you look... there is a bunch from 1-4, there is none from 5-7, and all of them are within 1-8, but the highest amount isn't at 3.
perimeter means to add up all the number around a surface so you are correct the answer is 12 because you are suppose to add up everything around the object so 7+5 which gives you 12