Question

Find the value of 1^3 + 2^3 +3^3 +4^3 +5^3 +6^3 using
the relationship between cubes, squares and
triangular numbers.​

Answer 1

Answer:

441

Step-by-step explanation:

The relationship referred to is:

  sum of the first n cubes = square of the n-th triangular number

In other words:

  sum of the first n cubes = square of the sum of the first n numbers

Symbolically:

  1³ + 2³ + 3³ + ... + n³ = ( 1 + 2 + 3 + ... + n )²

So what we need here is

  1³ + 2³ + 3³ + 4³ + 5³ + 6³

= ( 1 + 2 + 3 + 4 + 5 + 6 )²

= 21²

= 441

By the way, a formula for the n-th triangular number is n(n+1)/2.  So instead of adding the numbers from 1 to 6, we could have used this formula to get 1+2+3+4+5+6 = (6×7)/2 = 21.

Hope this helps!