Simplify the expasion of（1-x)^8+(1+x)^8 including the term in x^2,by putting x=0.01,find the approprizte value of 0.99^8
问题描述：
Simplify the expasion of（1-x)^8+(1+x)^8 including the term in x^2,by putting x=0.01,find the approprizte value of 0.99^8+1.01^8,correct to three decimal places.
答
（1-x)^8+(1+x)^8 = 2(1+8C2x^2 + 8C4x^4+8C6x^6+x^8)=2(1+ 28x^2+70x^4+28x^6+x^8)= 2+ 56x^2 ( including the term in x^2)x=0.010.99^8+1.01^8 = 2+56(0.01)^2=2.0056=2.006 ( 3decimal places)