MyQuestionIcon

1

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

Synthetic Division of Polynomials

Evaluate : ...

Question

Evaluate : $\frac{x + x^{2} + x^{3} + . . . . . . + x^{10}}{x - 1}$

Open in App

Solution

$x, x^{2}, x^{3}, . . ., x^{10}$ are in G.P
where $a = x, r = \frac{x^{2}}{x} = x$
$∴ S_{n} = \frac{a (r^{n} - 1)}{r - 1}$
$S = \frac{x + x^{2} + . . . . x^{10}}{x - 1} = \frac{x (x^{10} - 1)}{\frac{x - 1}{x - 1}} = \frac{x (x^{10} - 1)}{(x - 1)^{2}}$

Suggest Corrections

thumbs-up

0

Similar questions

\frac{1 - 2 x + x^{2}}{1 - x^{3}} \times \frac{1 + x + x^{2}}{1 + x}

Q. Evaluate lim_x->-1[1+x+x²+....+x¹⁰]

Q. If x is a proper fraction, show that

\frac{x}{1 - x^{2}} - \frac{x^{3}}{1 - x^{6}} + \frac{x^{5}}{1 - x^{10}} - . . . . . . . = \frac{x}{1 + x^{2}} + \frac{x^{3}}{1 + x^{6}} + \frac{x^{5}}{1 + x^{10}} + . . . . .

\int \frac{(x - 1) d x}{(x + 1) \sqrt{(x^{3} + x^{2} + x)}}

\int \frac{(x - 1)}{(x + 1) \sqrt{x^{3} + x^{2} + x}} d x

.

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Living Things Grow

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Synthetic Division of Polynomials

Standard IX Mathematics

Join BYJU'S Learning Program

CrossIcon