Numbers Game Help
Help Level 4c
Square a Series
Learn to Play the Numbers Game Level Four
Help with the Sigma summation to square then sum the series, for the Numbers Game level four.
Sigma Σ Sum Numbers Squared
The graphic above, represents Σ Sigma Squared or Sigma Squared.
ai2
The ai2 symbol,
to the right within the Σ Sigma Squared image,
represents each number as it's squared and summed.
To calculate the result of Σ Sigma Squared start with the lower limit. End with the upper limit. Square then add every digit from the lower to the upper limit.
i
The i variable displays below the Σ Sigma symbol. Again i equals one. The lower limit for this particular icon always equals one.
n
The player selects a digit which substitutes for the n.
Therefore i is the starting base number
and n is the ending base number.
Square each digit from i to n.
Then sum the result of each square.
Example
Assume the following question displays below the landscape.
Form an expression which evaluates to 5.
To find the correct answer
select 2, then tap the Σ Squared
symbol.
The expression
12 + 22 evaluates to 5.
12 = 1 22 = 4 1 + 4 = 5
Therefore 12 + 22
equals 1 + 4, and 1 + 4 = 5.
Your score increases by forty points.
However other correct expressions might exist.
Cheat Sheet for Sum of Squares
The domain for the Numbers Game
level four
is {1,2,3,4,5,6,7}.
The range for Sigma Σ Squared follows.
{
12,
12+22,
12+22+32,
12+22+32+42,
12+22+32+42+52,
12+22+32+42+52+62,
12+22+32+42+52+62+72
}
The sum of each range equals {1,5,14,30,55,91,140}.
Therefore Sigma Σ Squared calculates to
one of seven values from the set {1,5,14,30,55,91,140},
in level four of the Numbers Game
.
For details with factorials please see see Help with Factorials.
