Question

If $1^3+2^3+.........+9^3=2025,$, Then${\left(0.11\right)}^3+{\left(0.22\right)}^3+.......{\left(0.99\right)}^3$ will be-

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

Answer 1

The correct option is B 2.695

${(\cdot 11)}^3+{(\cdot 22)}^3+......+{(\cdot 99)}^3$
$={\left(\frac{11}{100}\right)}^3+{\left(\frac{22}{100}\right)}^3+...{\left(\frac{99}{100}\right)}^3$
$={\left(\frac{11}{100}\right)}^3[1^3+2^3+.......+a^3]$
$={\left(\frac{11}{100}\right)}^3\times 2025$
$[\because (1^3+2^3+a^3)=2025]$
(given)
$=\frac{1331}{1000000}\times 2025=2\cdot 69527$