Is the summed cubes equal to the squared sum of counting integer series?
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https://twitter.com/standupmaths/status/524470545199673344 R can tell us: DF.numbers = data.frame(cubesum=numeric(),sumsquare=numeric()) #initial dataframe for (n in 1:100){ #loop and fill in DF.numbers[n,"cubesum"] = sum((1:n)^3) DF.numbers[n,"sumsquare"] = sum(1:n)^2 } library(car) #for the scatterplot() function scatterplot(cubesum ~ sumsquare, DF.numbers, smoother=FALSE, #no moving average labels = rownames(DF.numbers), id.n = nrow(DF.numbers), #labels log = "xy", #logscales main = "Cubesum is identical to sumsquare, proven by induction") #checks that they are identical, except for the name all.equal(DF.numbers["cubesum"],DF.numbers["sumsquare"], check.names=FALSE)
Is the summed cubes equal to the squared sum of counting integer series?
Is the summed cubes equal to the squared sum…
Is the summed cubes equal to the squared sum of counting integer series?
https://twitter.com/standupmaths/status/524470545199673344 R can tell us: DF.numbers = data.frame(cubesum=numeric(),sumsquare=numeric()) #initial dataframe for (n in 1:100){ #loop and fill in DF.numbers[n,"cubesum"] = sum((1:n)^3) DF.numbers[n,"sumsquare"] = sum(1:n)^2 } library(car) #for the scatterplot() function scatterplot(cubesum ~ sumsquare, DF.numbers, smoother=FALSE, #no moving average labels = rownames(DF.numbers), id.n = nrow(DF.numbers), #labels log = "xy", #logscales main = "Cubesum is identical to sumsquare, proven by induction") #checks that they are identical, except for the name all.equal(DF.numbers["cubesum"],DF.numbers["sumsquare"], check.names=FALSE)