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Question

Which is larger, (1.01)1000000 or 10000?


Solution

We have

(1.01)1000000 or 10000

=(1.01)p10000, where 1000000 =p

=(1+0.01)p10000

=pC0+pC1×0.01+pC2×(0.01)2+....+pCp×(0.01)p10000

=1+(p×0.01)+[pC2×(0.01)2+...+(0.01)2+.....+(1.01)1000000]10000

=1+10000+[a positive real number]-10000

=1+(a positive real number)>0

Hence (1.01)1000000>10000


Mathematics

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