Use the principle of mathematical induction to prove the following formula. sum_(j=0)^n j^3=(n^2(n+1)^2)/4

Paloma Sanford

Paloma Sanford

Answered question

2022-10-24

Use the principle of mathematical induction to prove the following formula.
j = 0 n j 3 = n 2 ( n + 1 ) 2 4

Answer & Explanation

dkmc4175fl

dkmc4175fl

Beginner2022-10-25Added 15 answers

j = 0 n j 3 = n 2 ( n + 1 ) 2 4 n = 1 ,   L H S = 1 R H S = 1 2 ( 1 + 1 ) 2 4 = 1
Let L H S = j = 0 k + 1 = k 2 ( k + 1 ) 2 4 + ( k + 1 ) 3 = ( k + 1 ) 2 [ k 2 + 4 ( k + 1 ) ] 4 = ( k + 1 ) 2 ( k + 2 ) 2 ) 4 = ( k + 1 ) 2 ( ( k + 1 ) + 1 ) 2 4 = R H S

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