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If coefficients of three successive terms in the expansion of (x+1)n are in the ratio 1 : 3 : 5, then n is equal to
  • a)
    8
  • b)
    9
  • c)
    7
  • d)
    none of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If coefficients of three successive terms in the expansion of(x+1)nare...
To solve this problem, we need to use the concept of binomial expansion and the ratios of the coefficients. Let's break down the steps to find the value of 'n':

**Step 1: Understanding the Binomial Expansion**
The expansion of (x + 1)^n can be written as:
(x + 1)^n = C(n, 0) * x^n * 1^0 + C(n, 1) * x^(n-1) * 1^1 + C(n, 2) * x^(n-2) * 1^2 + ... + C(n, n) * x^0 * 1^n

Here, C(n, r) represents the binomial coefficient, which is given by the formula:
C(n, r) = n! / (r! * (n - r)!)

**Step 2: Understanding the Ratios**
According to the question, the coefficients of three successive terms are in the ratio 1 : 3 : 5. Let's assume the coefficients are a, b, and c, respectively.

So, we have:
a : b : c = 1 : 3 : 5

**Step 3: Finding the Ratios of Binomial Coefficients**
Using the formula for binomial coefficients, we can express the ratios of the coefficients in terms of the binomial coefficients:
a : b : c = C(n, 0) : C(n, 1) : C(n, 2)

We can simplify this further by using the formula for binomial coefficients:
a : b : c = 1 : n : (n * (n - 1)) / 2

**Step 4: Finding the Value of 'n'**
Now, we can equate the ratios of the coefficients to the given ratio:
1 : n : (n * (n - 1)) / 2 = 1 : 3 : 5

From this equation, we can find the value of 'n' by equating the corresponding terms:
n = 3

Therefore, the correct answer is option 'C' (7).
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If coefficients of three successive terms in the expansion of(x+1)nare in the ratio 1 : 3 : 5, then n is equal toa)8b)9c)7d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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