Expand (1+2x/3)8 in ascending powers of x up to the fourth term. Hence use your expansion to evaluate (0.98)8 to three significant figures.
1 + 8(2x/3) + 28(2x/3)2 + 56(2x/3)3= 1 + 16x/3 + 112x2/9 + 448x3/27(1 + 2x/3) = [ 1 + (-0.02)]2x/3 = -0.02x = -0.030.9881 + 16/3(-0.03) + 112/9(-0.03)2+ 448/27( -0.02)31 - 0.16 + 0.0112 - 0.000448= 0.851
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