Use the summation formulas to rewrite the expression without the summation notation. summation_k = 1^n 12k(k - 1) / n^3 Use the result to find the sums for n = 10, n= 100, n= 1000 n= 10,000.

For n=10:

Sum=3.96

For n=100:

Sum=3.9996

For n=1000:

Sum=3.999996

For n= 10000:

Sum=3.99999996

Step-by-step explanation:

Formula:

Rearranging the above formula:

           Eq (1)

According to summation formula:

Putt these in Eq (1), and we will get:

Taking as common:

After more simplifying,

Now ,for n=10:

For n=100:

For n=1000

For n=10000: