Question

if the sum of the cube of the first n consecutive natural number is 6084 the sum of those n numbers is​

Answer 1

Answer:

use the given formulae

Step-by-step explanation:

us assume the required sum = S

Therefore, S = 133 + 233 + 333 + 433 + 533 + ................... + n33

Now, we will use the below identity to find the value of S:

n44 - (n - 1)44 = 4n33 - 6n22 + 4n - 1

Substituting, n = 1, 2, 3, 4, 5, ............., n in the above identity, we get

                    144 - 044 = 4 ∙ 133 - 6 ∙ 122 + 4 ∙ 1 - 1

                    244 - 144 = 4 ∙ 233 - 6 ∙ 222 + 4 ∙ 2 - 1

                    344 - 244 = 4 ∙ 333 - 6 ∙ 322 + 4 ∙ 3 - 1

                    44