Binomial Theorem Applications
Using binomial theorem, (99)⁵ can be expressed as
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About This Question
- Subject
- mathematics
- Chapter
- binomial theorem and its simple applications
- Topic
- binomial theorem applications
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
(100 - 1)⁵
- Numerical Approximation: The binomial theorem is often used to calculate powers of numbers close to a multiple of 10 or 100.
- Breakdown: 99 is most easily represented as (100−1).
- Expansion: 995=(100−1)5=(05)1005−(15)1004+(25)1003−…
- This representation allows for easier mental or manual calculation of large powers by treating terms sequentially as powers of 100.
This easy difficulty mathematics question is from the chapter binomial theorem and its simple applications, covering the topic of binomial theorem applications. It appeared in the 2025 exam.
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