Question

Please answer this question

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

1+8+27+64+...+n³= 1/4* n²(n+1)², n≥1, n∈N

1. For n=1:

1³=1/4*1²(1+1)²=1/4*4=1- confirmed

2. For n=k, assume that:

1+8+27+64+...+k³= 1/4* k²(k+1)²

3. For n=k+1, prove that:

1+8+27+64+...+k³+(k+1)³= 1/4*(k+1)²(k+2)²

1+8+27+64+...+k³+(k+1)³=

1/4* k²(k+1)²+(k+1)³=

(k+1)²(1/4*k²+k+1)=

1/4*(k+1)²(k²+4k+4)=

1/4*(k+1)²(k+2)²----------- proved