How many terms are there in the expansion of (1 + x)^n?
Correct answer: C. n + 1
- A. 2^n
- B. n^
- C. n + 1
- D. n - 1
Explanation
Solution:The correct answer is c) n + 1.The expansion of (1 + x)^n can be written as:(1 + x)^n = 1 + nx + n(n-1)x^2/2! + n(n-1)(n-2)x^3/3! + ... + n!x^nThe number of terms in this expansion is n + 1, as there are n + 1 terms in the sum.Therefore, the number of terms in the expansion of (1 + x)^n is n + 1.
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Sequences describe ordered terms formed by a pattern, while series represent the sum of those terms. Questions cover arithmetic and geometric sequences, their nth terms, common difference or ratio, finite sums, and applications, with the sequence itself kept distinct from the corresponding series.
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