MyQuestionIcon

1

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

De-Moivre's Theorem

If α is the...

Question

If $α$ is the $n^{t h}$ root of unity, then $1 + 2 a + 3 a^{2} + . . .$ to $n$ terms equal to

A

\frac{- n}{(1 - α)^{2}}

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

B

\frac{- n}{1 - α}

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

C

\frac{- 2 n}{1 - α}

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

D

\frac{- 2 n}{(1 - α)^{2}}

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

Open in App

Solution

The correct option is B $\frac{- n}{1 - α}$
$S = 1 + 2 α + 3 α^{2} + . . . n α^{n - 1}$
$S (α) = α + 2 α^{2} + 3 α^{3} + . . . (n - 1) α^{n - 1} + n α^{n}$
$S (1 - α) = 1 + α + α^{2} + . . . α^{n - 1} - n α^{n}$
$S (1 - α) = \frac{1 - α^{n}}{1 - α} - n α^{n}$
$S (1 - α) = 0 - n$
$S = \frac{- n}{1 - α}$
$S = \frac{n}{α - 1}$

Suggest Corrections

thumbs-up

0

Similar questions

1, α, α^{2} . . . . . . α^{n}

n^{t h}

roots of unity then

^{n} C_{1} +^{n} C_{2} . α +^{n} C_{3} . α^{2} . . . . . . . . +^{n} C_{n} . α^{n}

1, α, α^{2} . . . . . α^{n - 1}

are n roots of unity then ,

1. α . α^{2} . . . . α^{n - 1}

α

n^{t h}

root of unity, then

1 + 2 α + 3 α^{2} + . . .

n

terms is equal to

1, α, α^{2}, . . . . ., α^{n - 1}

n^{t h}

roots of unity, then

(1 - α) (1 - α^{2}) . . . . . (1 - α^{n - 1})

α

n^{t h}

root of unity, then

1 + 2 α + 3 α^{2} + \dots

n

terms is equal to

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

De-Moivre's Theorem

MATHEMATICS

Watch in App

explore_more_icon

Explore more

De-Moivre's Theorem

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon