Question:
The total number of terms in the expansion of $ ( 1 + x ) ^{2n} - ( 1 - x ) ^{2n} $ after simplification is
The total number of terms in the expansion of $ ( 1 + x ) ^{2n} - ( 1 - x ) ^{2n} $ after simplification is
Updated On: Jan 12, 2024
- n + 1
- n - 1
- n
- 4n
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The Correct Option is C
Solution and Explanation
Answer (c) n
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Concepts Used:
Binomial Expansion Formula
The binomial expansion formula involves binomial coefficients which are of the form
(n/k)(or) nCk and it is calculated using the formula, nCk =n! / [(n - k)! k!]. The binomial expansion formula is also known as the binomial theorem. Here are the binomial expansion formulas.
This binomial expansion formula gives the expansion of (x + y)n where 'n' is a natural number. The expansion of (x + y)n has (n + 1) terms. This formula says:
We have (x + y)n = nC0 xn + nC1 xn-1 . y + nC2 xn-2 . y2 + … + nCn yn
General Term = Tr+1 = nCr xn-r . yr
- General Term in (1 + x)n is nCr xr
- In the binomial expansion of (x + y)n , the rth term from end is (n – r + 2)th .