Question

If $1^3+2^3+...+9^3=2025$, then $(0.11{)}^3+(0.22{)}^3+...(0.99{)}^3$ will be _________.

• A. 0.2695
• B. 3.695
• C. 2.695
• D. 0.3695

Answer 1

The correct option is C 2.695

Given: $1^3+2^3+...+9^3=2025$
$(0.11{)}^3+(0.22{)}^3+...+(0.99{)}^3=(0.11\times 1{)}^3+(0.11\times 2{)}^3+......+(0.11\times 9{)}^3=\left(0.11{)}^3\right[1^3+2^3+..{.9}^3]\Rightarrow 0.001331\times 2025=2.695275\approx 2.695$