4.3 SUM OF THE CUBES OF FIRST NATURAL NUMBERSEOREM Prove that : 1° +2

1.	4.3 SUM OF THE CUBES OF FIRST NATURAL NUMBERSEOREM Prove that : 1° +2° +33n(n+1)2OF Consider the identity(x + 1)* - *4x+6x2 + 4x + 1ting r = 1, 2, 3, ..., (n-1) and n successively, we get24 -1 = 4.13 +6.12 +4.1 + 134 -24 = 4.23 + 6.22 +4.2 +14* _ 34 = 4.33 +6.3² + 4. 3+1
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4.3 SUM OF THE CUBES OF FIRST NATURAL NUMBERSEOREM Prove that : 1° +2° +33n(n+1)2OF Consider the identity(x + 1)* - **4x+6x2 + 4x + 1ting r = 1, 2, 3, ..., (n-1) and n successively, we get24 -1* = 4.13 +6.12 +4.1 + 134 -24 = 4.23 + 6.22 +4.2 +14* _ 34 = 4.33 +6.3² + 4. 3+1

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4.3 SUM OF THE CUBES OF FIRST NATURAL NUMBERSEOREM Prove that : 1° +2° +33n(n+1)2OF Consider the identity(x + 1)* - **4x+6x2 + 4x + 1ting r = 1, 2, 3, ..., (n-1) and n successively, we get24 -1* = 4.13 +6.12 +4.1 + 134 -24 = 4.23 + 6.22 +4.2 +14* _ 34 = 4.33 +6.3² + 4. 3+1​

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4.3 SUM OF THE CUBES OF FIRST NATURAL NUMBERSEOREM Prove that : 1° +2° +33n(n+1)2OF Consider the identity(x + 1)* - **4x+6x2 + 4x + 1ting r = 1, 2, 3, ..., (n-1) and n successively, we get24 -1* = 4.13 +6.12 +4.1 + 134 -24 = 4.23 + 6.22 +4.2 +14* _ 34 = 4.33 +6.3² + 4. 3+1