Q:

In cross validation, higher the value of k, lesser the training data for this formula?

Is it right to say that smaller the value of k in cross validation based on the following formula, more the number of records in test data/smaller the number of records in training data.
According to me, these are the proportions of train and test data depending on the value of k for the following formula.
x.train = x.shuffle[which(1:nrow(x.shuffle)%%folds != i%%folds), ]
x.test = x.shuffle[which(1:nrow(x.shuffle)%%folds == i%%folds), ]

Proportion of train and test data depending on the value of k
At k==10, train:test = 9:1, ie, traindata = 90%, testdata = 10%
At k== 9, train:test = 8:1
At k== 8, train:test = 7:1
At k== 7, train:test = 6:1
At k== 6, train:test = 5:1
At k== 5, train:test = 4:1, ie, traindata = 80%, testdata = 20%
At k== 4, train:test = 3:1
At k== 3, train:test = 2:1
At k== 2, train:test = 1:1, ie, traindata = 50%, testdata = 50%
At k== 1, train:test = 0:1, ie, traindata =  0%, testdata = 100%

A:

Yes, you can say that (and your train/test ratios are also correct).
Although, $k=1$ doesn't really make sense. The most common choice is $k=10$ (paper reference [PDF]).

