Lf 1-x-x2n-r-02narxr- then a1-2a2-3a3-2na2n-

The correct option is D n (1+x+x^2)^n=∑ ^2n _r=0 a_r x^r Differentiating both the sides with respect to x , we get. n(1+x+x^2)^n 1(2x+1)=a_ ...

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

Sum of Coefficients of All Terms

lf 1+x+x2n=...

Question

lf $(1 + x + x^{2})^{n} = 2 n \sum r = 0 a_{r} x^{r}$ , then $a_{1} - 2 a_{2} + 3 a_{3} - \dots . - 2 n a_{2 n} = \dots$ .

0

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

1

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

n

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

- n

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

Open in App

Solution

Suggest Corrections

Similar questions

(1 + X + X^{2})^{n} = \sum_{r = 0}^{2 n} a_{r} x^{r}

a_{1} - 2 a_{2} + 3 a_{3} . . . . - 2 n a_{2 n}

a_{k}

x^{k}

(1 + x + x^{2})^{n}

k = 0, 1, 2,

\dots

2 n

a_{1} + 2 a_{2} + 3 a_{3} + \dots + 2 n a_{2_{n}} =

(1 + x + x^{2})^{n} = \sum_{r = 0}^{2 n} a_{r} x^{r}

a_{1} - 2 a_{2} + 3 a_{3} - \dots \dots - 2 n . a_{2 n} = \dots

p (x) = a_{0} + a_{1} x + . . . + a_{n} x^{n}

| p (x) | \leq ∣ ∣ e^{x - 1} - 1 ∣ ∣

x \geq 0,

| a_{1} + 2 a_{2} + 3 a_{3} + . . . + n a_{n} |

{(1 + x + x^{2} + \cdot \cdot + x^{n})}^{n}

= a_{0} + a_{1} x + a_{2} x^{2} + \cdot \cdot \cdot + a_{m p} x^{m p}

a_{1} + 2 a_{2} + 3 a_{3} + \cdot \cdot \cdot + n p a_{n p}

Join BYJU'S Learning Program