Question

1.  
   1. Expand the expression (1- ³/₁₀ x)⁵ in ascending powers of x, leaving coefficient as fractions in their lowest form.   
   2. Use the first three terms of the expansion in part (a) above to estimate the value (0.97)⁵

Answer 1

1. 1-5(^3x/₁₀) + 10(^3x/₁₀)² - 10(^3x/₁₀)³ + 5(^3x/₁₀)⁴ - (^3x/₁₀)⁵
   1- 1.5x + 0.9x² - 0.27x³ + 0.0405x⁴ - 0.00243x⁵
2. 0.975 = ( 1 - ³/₁₀x)5 
   x = 0.1
   1- 1.5x + 0.9x²  but x = 0.1
   1 - 1.5(0.1) + 0.9(0.1)² 
   = 0.859