# Sum of Series

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Excel BI’s Excel Challenge #318 — solved in R

### Defining the Puzzle:

Now we are asked to find sum of small series which value and number depends on input number itself. Sounds weird but it was suprisingly easy and nice.

Find the Sum of the Series — 1*2*3 + 2*3*4 + 3*4*5+…..+N*(N+1)*(N+2)

Hence, if N = 4

Then 1*2*3 + 2*3*4 + 3*4*5 + 4*5*6 = 210

For N = 8

1*2*3 + 2*3*4 + 3*4*5 + 4*5*6 + 5*6*7 + 6*7*8 + 7*8*9 + 8*9*10 = 1980

### Loading Data from Excel:

Lets start loading data and libraries:

library(tidyverse) library(readxl) input = read_excel(“Sum of Series.xlsx”, range = “A1:A10”) test = read_excel(“Sum of Series.xlsx”, range = “B1:B10”)

### Approach 1: Tidyverse with purrr

sum_of_products = function(N) { sum(map_dbl(1:N, ~ .x * (.x + 1) * (.x + 2))) } result = input %>% mutate(result = map_dbl(.$N,sum_of_products))

### Approach 2: Base R

sum_of_products <- function(N) { sum(sapply(1:N, function(x) x * (x + 1) * (x + 2))) } input$result <- sapply(input$N, sum_of_products)

### Approach 3: Data.table

As long as Base R and data.table will only differ in way of applying it on data.frame, I’ll drop DT. Sorry guys.

### Validation:

identical(test$`Expected Answer`, result$result) # [1] TRUE identical(test$`Expected Answer`, input$result) # [1] TRUE

If you like my publications or have your own ways to solve those puzzles in R, Python or whatever tool you choose, let me know.

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