Numbers Game Help

Help Level 4b

Sum a Series

Learn to Play the Numbers Game Level Four

Help with the Sigma summation for the Numbers Game level four.

Sigma Σ Sum Integers

The graphic above, represents summation of a series of numbers or Sigma Σ. Summation of a series of numbers involves simple addition. Start with the lower limit. End with the upper limit. Add every digit from the lower to the upper limit.

a_i

The a_i symbol, to the right of Sigma Σ indicates each number as it's summed.

n

The n, which displays above the Sigma Σ symbol, represents the upper limit or ending number.

i

The i, below the Sigma Σ symbol, represents the lower limit or starting number. Notice i equals one. The lower limit for this particular icon always equals one. However players select the upper limit.

To form an expression with Sigma Σ select a digit for the upper limit, then select the Sigma Σ symbol. The digit you select substitutes for n.

For example select the number 3 then the Sigma Σ symbol. The upper limit equals 3. The lower limit equals 1. The expression equals 1 + 2 + 3. The result equals 6 because 1 + 2 + 3 = 6.

Assume

Assume the following question displays below the landscape:

Form an expression which evaluates to 10.

To find the correct answer select 4, then tap the Sigma Σ symbol. The expression 1 + 2 + 3 + 4 evaluates to 10 because 1 + 2 + 3 + 4 = 10. Your score increases by forty points. However other correct expressions might exist.

Cheat Sheet for Sum of Integers

The domain for the Numbers Game is {1,2,3,4,5,6,7}. The range for Sigma Σ Sum of Numbers follows.

{
1,
1+2,
1+2+3,
1+2+3+4,
1+2+3+4+5,
1+2+3+4+5+6,
1+2+3+4+5+6+7
}

The result equals {1,3,6,10,15,21,28}. Therefore with level four of the Numbers Game, results for Sigma Σ Sum of Numbers calculate to one of seven values from the set {1,3,6,10,15,21,28}.

Formula for Sum of Integers

The formula Σn = [n x (n + 1)]/2 results in the sum from 1 to n integers. For example assume n = 6. [6 x (6 + 1)]/2 equals [6 x 7]/2 equals 42/2 equals 21. Notice the sixth entry in the set {1,3,6,10,15,21,28} also equals 21.