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In the context of the Binomial Theorem, which of the following statements is tru
In the context of the Binomial Theorem, which of the following statements is true?
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Practice Questions
1 question
Q1
In the context of the Binomial Theorem, which of the following statements is true?
The coefficients in the expansion are always positive.
The Binomial Theorem applies only to integers.
The expansion of (a + b)^n has n + 1 terms.
The theorem can only be applied when n is even.
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The expansion of (a + b)^n indeed has n + 1 terms, regardless of whether n is even or odd.
Questions & Step-by-step Solutions
1 item
Q
Q: In the context of the Binomial Theorem, which of the following statements is true?
Solution:
The expansion of (a + b)^n indeed has n + 1 terms, regardless of whether n is even or odd.
Steps: 5
Show Steps
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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