Question

5 cube+ 6 cube+7 cube.........+20cube

Answer 1

Answer:

8cube because we know that 7 after 8

Answer 2

Concept

The counting numbers that begin with 1 and go all the way to infinity are known as natural numbers. Finding the sum of the cubes of the first n natural numbers entails adding the cubes of a given number of natural numbers beginning with 1.

Sum (S) = (n(n + 1)/2)² can be used to find the sum of a series of cubes of n natural numbers, such as 1³ + 2³ + 3³ + 4³ +... + n³.

Given

Given a series 5³ + 6³ + 7³ + … + 20³.

Find

We have to find the sum of this given series.

Solution

Here, n = 20.

So, 1³ + 2³ + 3³ + 4³ + 5³ + 6³ + 7³ + … + 20³ = (20(20 + 1)/2)² = (10 * 21)² = (210)² = 44100.

i.e. 1 + 8 + 27 + 64 + 5³ + 6³ + 7³ + … + 20³ = 44100

i.e. 100 + 5³ + 6³ + 7³ + … + 20³ = 44100

i.e. 5³ + 6³ + 7³ + … + 20³ = 44100 - 100 = 44000

Therefore, the sum of the given series is 44000.

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