Verified answer

(0.99)^6

= (1 - 0.01)^6

= (1 - 0.01)^2 (1 - 0.01)^2 (1 - 0.01)^2

= 0.9801(0.9801)0.9801

= (0.9801)^3

= 0.941480149401

Coefficients: 1, 6, 15, 20, 15, 6, 1

0.99⁶ = (1-0.01)⁶

= 1(1⁶) - 6(1⁵·0.01) + 15(1⁴·0.01²) - 20(1³·0.01³) + 15(1²·0.01⁴) - 6(1·0.01⁵) + 1(0.01⁶)

= 1 - 6·10⁻² + 15·10⁻⁴ - 20·10⁻⁶ + 15·10⁻⁸ - 6·10⁻¹⁰ + 10¹²

= -0.06 + 0.0015 - 0.00002 + 0.00000015 - 0.0000000006 + 0.000000000001

You can finish from here

(a - b)^6 = a^6 - 6 * a^5 * b + 15 * a^4 * b^2 - 20 * a^3 * b^3 + 15 * a^2 * b^4 - 6 * a * b^5 + b^6

0.99^6 =>

(1 - 0.01)^6 =>

1^6 - 6 * 1^5 * 0.01 + 15 * 1^4 * 0.01^2 - 20 * 1^3 * 0.01^3 + 15 * 1^2 * 0.01^4 - 6 * 1 * 0.01^5 + 0.01^6 =>

1 - 6 * 1/100 + 15 * 1/10000 - 20 * 1/1000000 + 15 * 1/100000000 - 6 * 1/10000000000 + 1/1000000000000 =>

1 - 6/100 + 15/10000 - 20/1000000 + 15/100000000 - 6/10000000000 + 1/1000000000000

1 - 6/100 + 15/10000 - 20/1000000 =>

(1000000 - 60000 + 1500 - 20) / 1000000 =>

(940000 + 1480) / 1000000 =>

941480/1000000 =>

0.94148

0.941

0.99^6 = (1-0.01)^6

= 1^6+ 6C1*(-0.01)^1 + 6C2*(-0.01)^2 + 6C3*(-0.01)^3.....

= 1-0.06+0.0015-0.0002....

= 0.941