MyQuestionIcon

1

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

Sum of n Terms

If 1+x1+x21+x...

Question

If $(1 + x) (1 + x^{2}) (1 + x^{4}) \dots (1 + x^{128}) = n \sum r = 0 x^{r},$ then $n$ is equal to

A

256

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

B

255

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

C

254

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

D

257

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

Open in App

Solution

The correct option is B $255$
$(1 + x) (1 + x^{2}) (1 + x^{4}) \dots (1 + x^{128}) = n \sum r = 0 x^{r}$
Highest degree of $x$ on both sides,
$n = 1 + 2 + 4 + \dots \dots + 128 \Rightarrow n = 1 + 2 + 2^{2} + \dots \dots + 2^{7} \Rightarrow n = \frac{2^{8} - 1}{2 - 1} ∴ n = 255$

Suggest Corrections

thumbs-up

15

Similar questions

If $(1 + x) (1 + x^{2}) (1 + x^{4}) . . . (1 + x^{128}) = n \sum r = 0 x^{r},$ then n is equal to

(1 + x) (1 + x^{2}) (1 + x^{4}) \dots (1 + x^{128}) = n \sum r = 0 x^{r},

n

(1 + x) (1 + x^{2}) (1 + x^{4}) . . . (1 + x^{128}) = \sum_{r = 0}^{n} x^{r}

n

(1 + x) (1 + x^{2}) (1 + x^{4}) . . . . . (1 + x^{128}) = n \sum r = 0 x^{r}

then find the value of

n

(1 + x) (1 + x^{2}) (1 + x^{4}) . . . . (1 + x^{128}) = \sum_{r = 0}^{n} x^{r}

then findthe value of

n

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon