Question

Find the sum of the following series . 10^3+11^3+12^3+…+20^3

Answer 1

The sum of series is 42075

Step-by-step explanation:

To find the sum of $10^3+11^3+12^3+.......+20^3$

Let S = $10^3+11^3+12^3+.......+20^3$

As we know

$1^3+2^3+3^3+4^3+..........+n^3=( \dfrac{n(n+1)}{2} )^2$

Now

$10^3+11^3+12^3+.......+20^3 =( 1^3+2^3+3^3+........+20^3)- (1^3+2^3+3^3+........+9^3)$

Therefore by formula we have

$S =(\dfrac{20(20+1)}{2} )^2-(\dfrac{9(9+1)}{2} )^2\\\\\Rightarrow S=( 10\times 21)^2-( 9\times 5)^2= 210^2- 45^2= 42075$

Hence , the sum of series is 42075

#Learn more

Find the sum of cubes of natural numbers from 10 to 20

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Answer 2

Answer:

find the sum :10³+11³+12³+....+20³