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If the Binomial Theorem is applied to (x + 1)^n, what is the sum of the coeffici
If the Binomial Theorem is applied to (x + 1)^n, what is the sum of the coefficients of the expansion?
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Q1
If the Binomial Theorem is applied to (x + 1)^n, what is the sum of the coefficients of the expansion?
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1
n
2^n
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The sum of the coefficients in the expansion of (x + 1)^n is found by substituting x = 1, which gives 2^n.
Questions & Step-by-step Solutions
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Q
Q: If the Binomial Theorem is applied to (x + 1)^n, what is the sum of the coefficients of the expansion?
Solution:
The sum of the coefficients in the expansion of (x + 1)^n is found by substituting x = 1, which gives 2^n.
Steps: 6
Show Steps
Step 1: Understand that the Binomial Theorem helps us expand expressions like (x + 1)^n.
Step 2: The coefficients in the expansion are the numbers in front of each term when we write out (x + 1)^n.
Step 3: To find the sum of all these coefficients, we can substitute x with 1 in the expression.
Step 4: Substitute x = 1 into (x + 1)^n, which gives us (1 + 1)^n.
Step 5: Simplify (1 + 1)^n to get 2^n.
Step 6: Therefore, the sum of the coefficients in the expansion of (x + 1)^n is 2^n.
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