Question

Prove that General term in the expansion of(x+1/x)^13
is 13 cr x^13-2r. Hence find 12th term
​

Answer 1

Answer:

mujhe bhi iska hi answer chhiye koi jaldi dedo yrr please help karo hamari

Answer 2

Answer:

The general term is ¹³Cₐ $x^{n-2a}$ and the 12th term is 13 x⁻¹¹.

Step-by-step explanation:

Given,

The binomial expansion:

(x + 1/x)¹³

To find,

The general term, and the 12th term in the series.

Calculation,

(x + 1/x)¹³ = ¹³C₁ x¹³(1/x)⁰ + ¹³C₂ x¹²(1/x)¹ +.........+ ¹³C₁₃ x⁰(1/x)¹³.

As from above, we can see that if the number of terms is increasing, then the power of x is decreasing and the power of (1/x) is increasing.

So, ath term is ¹³Cₐ xⁿ⁻ᵃ (1/x)ᵃ

⇒ ath term = ¹³Cₐ xⁿ⁻ᵃ (x⁻ᵃ)

⇒ ath term = ¹³Cₐ $x^{n-2a}$

Therefore, the general term in the binomial expression (x + 1/x)¹³ is  ¹³Cₐ$x^{n-2a}$.

Now, for the 12th term:

a = 12

⇒ 12th term = ¹³C₁₂ x¹³⁻²⁴

⇒ 12th term = 13 x⁻¹¹

Therefore, the 12th term is 13 x⁻¹¹.

#SPJ2