Average value of the highest roll of a, i-sided dice
Expression 6: "i" equals 20i=20
negative 10−10
2020
6
Riemann sum where each term is the amount of a scenarios in which a certain value is the highest possible roll (The sum of terms is equal to the total possible rolls)
7
Expression 8: Start sum from "n" equals 0 to "i" minus 1, end sum, left parenthesis, left parenthesis, 1 plus left parenthesis, left parenthesis, "i" minus 1 , right parenthesis minus "n" , right parenthesis , right parenthesis Superscript, "a" , Baseline minus left parenthesis, left parenthesis, "i" minus 1 , right parenthesis minus "n" , right parenthesis Superscript, "a" , Baseline , right parenthesisi−1∑n=01+i−1−na−i−1−na
equals=
400400
8
Riemann sum where each term is the product of the amount of times a certain value is the highest rolled number and the number rolled
9
Expression 10: Start sum from "n" equals 0 to "i" minus 1, end sum, left parenthesis, left parenthesis, left parenthesis, 1 plus left parenthesis, left parenthesis, "i" minus 1 , right parenthesis minus "n" , right parenthesis , right parenthesis Superscript, "a" , Baseline minus left parenthesis, left parenthesis, "i" minus 1 , right parenthesis minus "n" , right parenthesis Superscript, "a" , Baseline , right parenthesis times left parenthesis, "i" minus "n" , right parenthesis , right parenthesisi−1∑n=01+i−1−na−i−1−na·i−n
equals=
55305530
10
y = the average high roll of x, i-sided dice
11
Expression 12: "y" equals StartFraction, Start sum from "n" equals 0 to "i" minus 1, end sum, left parenthesis, left parenthesis, left parenthesis, 1 plus left parenthesis, left parenthesis, "i" minus 1 , right parenthesis minus "n" , right parenthesis , right parenthesis Superscript, "x" , Baseline minus left parenthesis, left parenthesis, "i" minus 1 , right parenthesis minus "n" , right parenthesis Superscript, "x" , Baseline , right parenthesis times left parenthesis, "i" minus "n" , right parenthesis , right parenthesis Over Start sum from "n" equals 0 to "i" minus 1, end sum, left parenthesis, left parenthesis, 1 plus left parenthesis, left parenthesis, "i" minus 1 , right parenthesis minus "n" , right parenthesis , right parenthesis Superscript, "x" , Baseline minus left parenthesis, left parenthesis, "i" minus 1 , right parenthesis minus "n" , right parenthesis Superscript, "x" , Baseline , right parenthesis , EndFractiony=i−1∑n=01+i−1−nx−i−1−nx·i−ni−1∑n=01+i−1−nx−i−1−nx