Question

2³+2³+3³+...........+10³=
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Answer 1

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1³+2³+3³+...........+10³=

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It is given, 1³ + 2³ + 3³ + ... + 10³ = 3025 ........( 1 )

Now, 2³ + 4³ + 6³ + ... + 20³ = (1 × 2)³ + (2 × 2)³ + (2 × 3)³ + ... + (2 × 10)³

2³ + 4³ + 6³ + ... + 20³ = 2³ [1³ + 2³ + 3³ + ... + 10³]

Using the value of equation ( 1 ) , we get

∴ 2³ + 4³ + 6³ + ... + 20³ = 8 × 3025 = 24200

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Answer 2

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• Find the value of ${2}^{3} + {3}^{3} + ....... + {10}^{3}$

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Sum of cubes of natural number is calculated by the formula,

${1}^{3} + {2}^{3} + ....+ {n}^{3} = {( \frac{n(n + 1)}{2}) }^{2}$

So,

${1}^{3} + {2}^{3} + {3}^{3} + ....... + {10}^{3} = {( \frac{10 \times 11}{2} )}^{2}$

$= {55 }^{2}$

$= 3025$

So,

${1}^{3} + {2}^{3} + {3}^{3} + ....... + {10}^{3} = 3025$

$\implies {2}^{3} + {3}^{3} + ....... + {10}^{3} = 3025 - 1$

$\implies {2}^{3} + {3}^{3} + ....... + {10}^{3} = 3024$

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• Answer for the problem is =3024.