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In the context of the Binomial Theorem, which of the following statements is tru

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Question: In the context of the Binomial Theorem, which of the following statements is true?

Options:

  1. The coefficients in the expansion are always positive.
  2. The Binomial Theorem applies only to integers.
  3. The expansion of (a + b)^n has n + 1 terms.
  4. The theorem can only be applied when n is even.

Correct Answer: The expansion of (a + b)^n has n + 1 terms.

Solution: 

The expansion of (a + b)^n indeed has n + 1 terms, regardless of whether n is even or odd.

In the context of the Binomial Theorem, which of the following statements is tru

Practice Questions

Q1
In the context of the Binomial Theorem, which of the following statements is true?
  1. The coefficients in the expansion are always positive.
  2. The Binomial Theorem applies only to integers.
  3. The expansion of (a + b)^n has n + 1 terms.
  4. The theorem can only be applied when n is even.

Questions & Step-by-Step Solutions

In the context of the Binomial Theorem, which of the following statements is true?
  • Step 1: Understand what the Binomial Theorem is. It helps us expand expressions like (a + b)^n.
  • Step 2: Identify what 'n' represents. It is a non-negative integer (0, 1, 2, 3, ...).
  • Step 3: Recognize that when we expand (a + b)^n, we are combining 'a' and 'b' in different ways.
  • Step 4: Count the number of terms in the expansion. The number of terms is always one more than 'n'.
  • Step 5: Conclude that for any value of 'n', whether it is even or odd, the expansion will have n + 1 terms.
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