Math, asked by sarthak4254K, 7 months ago

2³+2³+3³+...........+10³=

Answers

Answered by Anonymous
83

\huge\mathbb\green{Question:-}

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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Answered by anindyaadhikari13
18

\star\:\:\:\bf\large\underline\blue{Question:-}

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

\star\:\:\:\bf\large\underline\blue{Solution:-}

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

\star\:\:\:\bf\large\underline\blue{Answer:-}

  • Answer for the problem is =3024.
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