The expansion 1-xn - 1 - nx - nn-1-2-x2- is valid if -x- - 1-

It is valid only if |x| lt; 1 The expansion (1+x)^n = 1 + nx + n(n 1)/2!(x)^2......... has infinite number of terms. If |x| gt; 1, the value on the R. ...

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

Byju's Answer

Standard XIII

Mathematics

Binomial Theorem for Any Index

The expansion...

Question

The expansion ${(1 + x)}^{n}$ = 1 + nx + $\frac{n (n - 1)}{2!}$ ${(x)}^{2}$ ........... is valid if |x| > 1.

True

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

False

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

Open in App

Solution

The correct option is B
False

It is valid only if |x| < 1

The expansion ${(1 + x)}^{n}$ = 1 + nx + $\frac{n (n - 1)}{2!}$ ${(x)}^{2}$ ......... has infinite number of terms. If |x| > 1, the value on the R.H.S might become infinite. L.H.S. will always be finite if n is finite. E.g.: consider ${(1 + 1)}^{n}$ = 1 + n + $\frac{n (n - 1)}{2!}$ ........ L.H.S. is 2n but R.H.S. will be infinite. So we want |x| < 1.

Suggest Corrections

Similar questions

The expansion ${(1 + x)}^{n}$ = 1 + nx + $\frac{n (n - 1)}{2!}$ ${(x)}^{2}$ ........... is valid if |x| > 1.

Q. If x₁,x₂,x₃,x₄….x_2n+1are in Arithmetic Progression, then find the value of [(x_2n+1–x₁)/ (x_2n+1+x₁)] + [(x_2n–x₂)/ (x_2n–x₂)]………….. [(x_n+2–x_n)/ (x_n+2–x_n)]

Q. Show that

lim x \to 1 \frac{x + x^{2} + x^{3} + . . . . + x^{n} - n}{x - 1}

\frac{n (n + 1)}{2}

Q. If

| x | < 1

, then the coefficient of

x^{n}

in the expansion

{(1 + x + x^{2} + x^{3} + . . .)}^{2}

Q. If

| x | < 1

then the coefficient of

x^{n}

in expansion of

{(1 + x + x^{2} + x^{3} . . . .)}^{2}

Join BYJU'S Learning Program

The expansion (1+x)n = 1 + nx + n(n−1)2!(x)2........... is valid if |x| > 1.

The expansion ${(1 + x)}^{n}$ = 1 + nx + $\frac{n (n - 1)}{2!}$ ${(x)}^{2}$ ........... is valid if |x| > 1.