Math Problem Statement
Find the first five terms, in ascending powers of 𝑥, in the expansion of (1 + 𝑥)^7
Solution
To find the first five terms in the expansion of , we can use the Binomial Theorem, which states that:
Where:
- is the binomial coefficient, given by .
- in this case.
We'll calculate the first five terms (i.e., up to ).
-
For :
-
For :
-
For :
-
For :
-
For :
Thus, the first five terms in the expansion of are:
Would you like more details or have any questions? Here are five related questions to explore further:
- How is the binomial coefficient calculated in general?
- What is the full expansion of ?
- What would the expansion look like for negative exponents, such as ?
- How can the binomial theorem be applied to higher-order powers, like ?
- What is the general formula for the expansion of ?
Tip: The binomial theorem is a powerful tool for expanding expressions of the form , and it is used extensively in algebra and calculus for approximation techniques!
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Math Problem Analysis
Mathematical Concepts
Algebra
Binomial Expansion
Polynomial Expansions
Formulas
Binomial Theorem: (1 + x)^n = Σ (n choose k) x^k
Theorems
Binomial Theorem
Suitable Grade Level
Grades 10-12