Question

Find an approximation of (0.99) 5 using the first three terms of its expansion.

Answer 1

The given expression is ( 0.99 ) 5

We can write 0.99 as 0.99=1−0.01

Expanding the given expression using Binomial Theorem ( 0.99 ) 5 = ( 1−0.01 ) 5 =( C 5 0 ( 1 ) 5−0 ( 0.01 ) 0 − C 5 1 ( 1 ) 4 ( 0.01 ) 1 + C 5 2 ( 1 ) 3 ( 0.01 ) 2 − C 5 3 ( 1 ) 2 ( 0.01 ) 3 + C 5 4 ( 1 ) 1 ( 0.01 ) 4 − C 5 5 ( 1 ) 0 ( 0.01 ) 5 ) =1−5( 0.01 )+10 ( 0.01 ) 2 −10 ( 0.01 ) 3 +5 ( 0.01 ) 4 −1 ( 0.01 ) 5 =1−0.05+0.001−0.00001+0.0000005−0.000000001 =0.951 [Approximately]

Thus, the value of ( 0.99 ) 5 is approximately 0.951 .