Sum of n terms of the series:

To find the sum of n terms of the given series, we can use the concept of expansion of binomial expressions. The given series can be written as:

(4 - 1/n) * (4 - 2/n) * (4 - 3/n) * ...

Expanding the series:

Let's expand the first few terms of the given series:

(4 - 1/n) * (4 - 2/n) = 16 - 8/n - 4/n + 2/n^2

We can observe that the terms with 'n' in the denominator will cancel out when multiplied together, leaving us with:

16 - 8/n - 4/n + 2/n^2

Similarly, expanding the first three terms of the series:

(4 - 1/n) * (4 - 2/n) * (4 - 3/n) = (16 - 8/n - 4/n + 2/n^2) * (4 - 3/n)
= 64 - 32/n - 16/n + 8/n^2 - 48/n + 24/n^2 + 12/n^2 - 6/n^3

Again, we can simplify the terms with 'n' in the denominator:

64 - 32/n - 16/n + 8/n^2 - 48/n + 24/n^2 + 12/n^2 - 6/n^3
= 64 - 80/n + 44/n^2 - 6/n^3

Generalizing the pattern:

By observing the pattern in the expansion, we can generalize the terms as follows:

The sum of n terms of the series can be written as:
S(n) = 64 - 80/n + 44/n^2 - 6/n^3

Summary:

The sum of n terms of the series (4 - 1/n) * (4 - 2/n) * (4 - 3/n) can be found using the expanded form of the series. By generalizing the pattern, we obtain the formula S(n) = 64 - 80/n + 44/n^2 - 6/n^3, which represents the sum of n terms.