Question

find the Sum: please say​

Answer 1

Step-by-step explanation:

Given :-

11^3+12^3+....+18^3

To find:-

Find the sum of 11^3+12^3+....+18^3

Solution:-

Given that

11^3+12^3+....+18^3

It can be written as

(1^3+2^3+3^3+...+18^3)-(1^3+2^3+...+10^3)

We know that

The sum of the cubes of the first n natural numbers = [n(n+1)/2]^2

We have n = 18 (in first part)

n=10 ( in second part)

Using this formula then

=>[18(18+1)/2]^2 - [10(10+1)/2]^2

=> [18(19)/2]^2 - [10(11)/2]^2

=> (9×19)^2 - (5×11)^2

=> (171)^2 - (55)^2

=>29241 - 3025

=> 26,216

Answer:-

The sum of 11^3+12^3+....+18^3 = 26216

Used formulae:-

• The sum of the cubes of the first n natural numbers = [n(n+1)/2]^2