The number of terms in the expansion of x 2-1-1- x 2 n - n - N- isA- 2 nB- 3 nC- 2 n-1D- 3 n -1

The correct option is C 2n+1 [ 1 + ( x^2 + 1/x^2) ]^n = ^nC_o + ^nC_1( x^2 + 1/x^2) + ^nC_2 ( x^2 + 1/x^2)^2 + ^nC_3 ( x^2 + 1/x^2)^3 .............^nC_n ( x^2 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

General Term of Binomial Expansion

The number of...

Question

The number of terms in the expansion of ${(x^{2} + 1 + \frac{1}{x^{2}})}^{n}, n \in$ N, is

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2n+1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

3n+1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C
2n+1

${[1 + (x^{2} + \frac{1}{x^{2}})]}^{n}$ = $^{n} C_{o}$ + $^{n} C_{1}$ $(x^{2} + \frac{1}{x^{2}})$ + $^{n} C_{2}$ ${(x^{2} + \frac{1}{x^{2}})}^{2}$ + $^{n} C_{3}$ ${(x^{2} + \frac{1}{x^{2}})}^{3}$ ............. $^{n} C_{n}$ ${(x^{2} + \frac{1}{x^{2}})}^{n}$

there 2 distinct terms corresponding to each factor $\Rightarrow$ hence total number of terms 2n+1.

Suggest Corrections

Similar questions

Q. The total number of terms which are dependent on the value of

x

, in the expansion

{(x^{2} - 2 + \frac{1}{x^{2}})}^{n}, n \in N

is equal to

The (n+1)th term from the end in the expansion of $(2 x - \frac{1}{x})^{3 n}$ is:

Q. The

n^{th}

term in the expansion of

{log}_{e} (\frac{4}{3})

If f (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 + x^{n} & (1 - x)^{n} & 2 + x^{n} (2 + x)^{n} & (2 + x)^{n} & 1 (3 - x)^{n} & 1 & 3 + x \end{matrix} ∣ ∣ ∣ ∣ ∣

then the constant term in the expansion is

Q. The number of terms in the expansion of

{(x^{2} + 1 + \frac{1}{x^{2}})}^{n}, n \in N

is-

Join BYJU'S Learning Program

The number of terms in the expansion of (x2+1+1x2)n,n∈ N, is

The correct option is C 2n+1 [1+(x2+1x2)]n = nCo + nC1(x2+1x2) + nC2 (x2+1x2)2 + nC3 (x2+1x2)3 .............nCn (x2+1x2)n there 2 distinct terms corresponding to each factor ⇒ hence total number of terms 2n+1.

The number of terms in the expansion of ${(x^{2} + 1 + \frac{1}{x^{2}})}^{n}, n \in$ N, is