binomial theorem applications

Question

Using binomial theorem, (99)⁵ can be expressed as

RankGuru · Accepted Answer

1. **Numerical Approximation**: The binomial theorem is often used to calculate powers of numbers close to a multiple of 10 or 100.
2. **Breakdown**: $99$ is most easily represented as $(100 - 1)$.
3. **Expansion**: $99^5 = (100 - 1)^5 = \binom{5}{0}100^5 - \binom{5}{1}100^4 + \binom{5}{2}100^3 - \dots$
- This representation allows for easier mental or manual calculation of large powers by treating terms sequentially as powers of $100$.

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