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Algebra Level 2

1 3 + 2 3 + 3 3 + . . . . . . + 3 0 3 ? 1^3 + 2^3 + 3^3 + ...... +30^3?

157895 20090 216225 200495 27305

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Irfan Wahyudin by Irfan Wahyudin , 22, Indonesia

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3 solutions

Irfan Wahyudin
Jan 19, 2015

1 3 + 2 3 + 3 3 + . . . + 3 0 3 = ( 1 + 2 + 3 + . . . . + 30 ) 2 = ( 31 × 15 ) 2 = 216225 1^3 + 2^3 + 3^3 + ... + 30^3\\= (1+2+3+....+30)^2\\= (31\times 15)^2\\= 216225

4 Helpful 0 Interesting 0 Brilliant 0 Confused

@Irfan Wahyudin I have fixed LaTeX in your question and solution. Check them once for accuracy. You may use these LaTeX as reference in future.

Pranjal Jain - 6 years, 4 months ago

for the sum for cubes of first N natural numbers: (n(n+1))^2

1 Helpful 0 Interesting 0 Brilliant 1 Confused
Sunil Pradhan
Jan 20, 2015

1³ + 2³ + 3³ + .... + n³ = [n(n+1)/2]²

= [30(30+1)/2]² = 216225

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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