Question

I need to know number 7 it says find the sum of the first 9 terms

Answer 1

Given:

`1+8+27+64+125+.....`

To find:

The sum of the first 9 terms

Step-by-step explanation:

The series is of the form,

`1^3+2^3+3^3+4^3+5^3+......`

Using the formula,

`1^3+2^3+.....+n^3=((n(n+1))/(2))^2`

Here, n = 9.

On substitution we get,

`\begin{gathered} 1^3+2^3+......+^3=((9(9+1))/(2))^2 \\ =((9(10))/(2))^2 \\ =((90)/(2))^2 \\ =45^2 \\ =2025 \end{gathered}`

Final answer:

The sum of the first 9 terms is 2025.