Alg10.16

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Find the value of (0.99)^9\, corrected to 4 decimals using teh binomial theorm.

(0.99)^9=(1-0.01)^9=1-9\!C_1 (0.01)+9\!C_2 (0.01)^2-9\!C_3 (0.01)^3+9\!C_4 (0.01)^4-9\!C_5 (0.01)^5+9\!C_6 (0.01)^6-9\!C_7 (0.01)^7+9\!C_8 (0.01)^8-9\!C_9 (0.01)^9\,

1-9(0.01)+36(0.01)^2-84(0.01)^3+126(0.01)^4-126(0.01)^5+84(0.01)^6-36(0.01)^7+9(0.01)^8-(0.01)^9\,

0.9136\,


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