Find the first 4 terms in the expansion of (1 + x 2) 8. Use your answer to find the value of (1.01) 8

(1+x^2) ^8

= (1+8x^2+8*7 / (1*2) x^4+8*7*6 / (1*2*3) x^6+8*7*6*5 / (1*2*3*4) x^8 + ...)

=1+8x^2+28x^4+56x^6+70x^8 + ...)

For x<1, higher power terms diminish in value, hence we can approximate powers of numbers.

1.01 = (1+0.1^2) = > x=0.1 in the above expansion

(1.01) ^8

=1+8 (0.1^2) + 28 (0.1^4) + 56 (0.1^6) [ limited to four terms, as requested]

=1+0.08+0.0028+0.000056 (+0.00000070)

=1.082856 (approximately)