Observe the following pattern:
$1^{3}=1$
$1^{3}+2^{3}=(1+2)^{2}$
$1^{3}+2^{3}+3^{3}=(1+2+3)^{2}$
Write the next three rows and calculate the value of $1^3 + 2^3 + 3^3 +…. + 9^3 + 10^3$ by the above pattern.


Given:

                    $1^{3}=1$

          $1^{3}+2^{3}=(1+2)^{2}$

$1^{3}+2^{3}+3^{3}=(1+2+3)^{2}$

To do:

We have to write the next three rows and calculate the value of $1^3 +2^3 + 3^3 +…. + 9^3 + 10^3$ by the above pattern.

Solution:  

The next three terms of the given pattern are:

$1^{3}+2^{3}+3^{3}+4^{3}=(1+2+3+4)^{2}$

$1^{3}+2^{3}+3^{3}+4^{3}+5^{3} =(1+2+3+4+5)^{2}$

$1^{3}+2^{3}+3^{3}+4^{3}+5^{3}+6^{3}=(1+2+3+4+5+6)^{2}$

Therefore,

$1^{3}+2^{3}+3^{3}+\ldots .+9^{3}+10^{3}=(1+2+3+\ldots .+9+10)^{2}$

$=55^2$

$=3025$

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Updated on: 10-Oct-2022

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