#The original purpose for creating this functions
#was considering a mathematical problem of prooving
#the fact that (n!)/(2^n) is not an integer number
#The idea was that some fraction of multipliers in denominator
#are cancelled by even numbers in n!, so that only odd
#numbers are left in numerator.
#That leads to dividing an odd number by even number,
#which gives us a nonintegral number
#So we need a formula to calculate product
#of even numbers in numerator.
#If it turn ot that the product of even numbers in numerator
#is greater then denominator, then (n!)/(2^n) seems to be
#inevitably integer
#In fact, i (the author of program) did not succeed
#in deriving a formula for the product of even numbers in n!
#evenProduct(num) gives product of all even positive integers
#less then or equal to num
evenProduct <- function (num) {
product <- 1
for(i in 1:num) {
if ((i %% 2) == 0) product <- product * i
}
if (product == 1) product <- 0
product
}
#evenProduct(num) gives sum of all even positive integers
#less then or equal to num
evenSum<- function (num) {
sum <- 0
for(i in 1:num) {
if ((i %% 2) == 0) sum <- sum + i
}
sum
}
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even-Product-Sum.zip_SUM
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R code. There are two functions: evenProduct(num) gives product of all even positive integers less then or equal to num evenProduct(num) gives sum of all even positive integers less then or equal to num
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