Expand (2 + 2x)5 in ascending powers of x up to the term x3

      

a) Expand (2 + 2x)5 in ascending powers of x up to the term x3
b) Hence use your expansion in a) above to evaluate (2.03)5 to 3 s.f.

  

Answers


John
a) (2 + 2x)5

There are 6 terms

$2^5 \; + \; 5(2)^4 (2x)^1 \; + \; 10(2)^3(2x)^2 \; +\; 10(2)^2 (2x)^3$ + …………

Simplifies to

$32 + 160x + 320x^2 + 320x^3$ + ………………..

(2x = 0.03;) x = 0.015

32 + 160(0.015)2

+ 320(0.015)3 + ………….

32. + 2.4 + 0.072 + 0.00108 + ……….

34.473

34.5 correct to 3 s.f
johnmulu answered the question on March 7, 2017 at 13:13


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