Given:
[tex]1+8+27+64+125+.....[/tex]
To find:
The sum of the first 9 terms
Explanation:
The series is of the form,
[tex]1^3+2^3+3^3+4^3+5^3+......[/tex]
Using the formula,
[tex]1^3+2^3+.....+n^3=(\frac{n(n+1)}{2})^2[/tex]
Here, n = 9.
On substitution we get,
[tex]\begin{gathered} 1^3+2^3+......+^3=(\frac{9(9+1)}{2})^2 \\ =(\frac{9(10)}{2})^2 \\ =(\frac{90}{2})^2 \\ =45^2 \\ =2025 \end{gathered}[/tex]
Final answer:
The sum of the first 9 terms is 2025.
