Question

derive the formulae of sum of first natural conescutive number's cube
(n(n+1)/2)^2​

Answer 1

Answer:

The series \sum\limits_{k=1}^n k^a = 1^a + 2^a + 3^a + \cdots + n^a  

k=1 ∑ n ​   k  a  =1  a  +2  a  +3  a  +⋯+n  a

 gives the sum of the a^\text{th}a  th

 powers of the first nn positive numbers, where aa and nn are positive integers. Each of these series can be calculated through a closed-form formula. The case a=1,n=100a=1,n=100 is famously said to have been solved by Gauss as a young schoolboy: given the tedious task of adding the first 100100 positive integers, Gauss quickly used a formula to calculate the sum of 5050.5050.

Answer 2

Step-by-step explanation:

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