Question 1135125: Write the sum using summation notation, assuming the suggested pattern continues.
100 + 121 + 144 + 169 + ... + n2 + ... (2 points)
choices are below
summation of n squared from n equals eleven to infinity
summation of n minus one squared from n equals ten to infinity
summation of n squared from n equals ten to infinity
summation of n plus one squared from n equals ten to infinity
Answer by greenestamps(13215)   (Show Source):
You can put this solution on YOUR website!
The answer choices are all very similar, showing the summation of squares going to infinity. Which of the choices makes the first term of the sequence equal to 100 (=10 squared)?
(1) summation of n squared from n equals eleven to infinity
In the summation of (n squared) with 11 as the initial value, the first term is 11^2
(2) summation of n minus one squared from n equals ten to infinity
In the summation of ((n-1) squared) with 10 as the initial value, the first term is (10-1)^2 = 9^2
(3) summation of n squared from n equals ten to infinity
In the summation of (n squared) with 10 as the initial value, the first term is 10^2
(4) summation of n plus one squared from n equals ten to infinity
In the summation of ((n+1) squared) with 10 as the initial value, the first term is (10+1)^2 = 11^2
The correct summation is clearly choice 3.
But you will very often see summations similar to the other choices; there might be a good reason, in a particular problem, to define the summation in a way that doesn't seem the easiest. For example, another summation that produces the given sequence could be
summation of (n+4) squared from n equals six to infinity
or
summation of (n+9) squared from n equals one to infinity
|
|
|
