Which is larger \((1.01)^{1000000}\) or 10,000?

Solution :

We have, \((1.01)^{1000000}\)  – 10000

= \((1 + 0.01)^{1000000}\) – 10000

By using binomial theorem,

= \(^{1000000}C_0\) + \(^{1000000}C_1 (0.01)\)  + \(^{1000000}C_2 (0.01)^2\)  + …… + \(^{1000000}C_{1000000} (0.01)^{1000000}\) – 10000

= (1 + 1000000(0.01) + other positive terms) – 10000

= (1 + 10000 + other positive terms) – 10000

= 1 + other positive terms > 0

Hence,  \((1.01)^{1000000}\) is greater than 10000.


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