Express the series using sigma notation. 2 - 6 + 18 – 54 + 162 ...

Mathematics

1 answer:

lidiya [134]3 years ago

6 0

$2-6+18-54+162+\cdots=2(-3)^0+2(-3)^1+2(-3)^2+2(-3)^3+2(-3)^4+\cdots$
$=\displaystyle2\sum_{n=0}^\infty(-3)^n$

You might be interested in

what algebraic expression must be added to the sum of 3x squared + 4x + 8 and 2x squared -6x + 3 to give 9x squared -2x - 5 as t

gregori [183]

<span>3x^2 + 4x + 8 + 2x^2 - 6x + 3 to give result as 9x^2 -2x - 5

</span>3x^2 + 4x + 8 + 2x^2 - 6x + 3
= 5x^2 - 2x + 11

so

9x^2 -2x - 5 - (5x^2 - 2x + 11)
= 9x^2 -2x - 5 - 5x^2 + 2x - 11
= 4x^2 -16

answer

expression (4x^2 -16) must be added to the sum of (3x^2 + 4x + 8) and (2x^2 - 6x + 3) to give the result as (9x^2 - 2x - 5)

3 0

3 years ago

The perimeter of a rectangular pool is 326 M if the length of the pool is 87 M what is its width

sveta [45]

Half the perimeter is equal to the length plus the width.

326 /2 = 163

Length + width = 163

87 + width = 163

Width = 163 - 87

Width = 76 meters

4 0

2 years ago

I need help on solving these types of geometry problems! Teacher said the answer is 7 but I have to show work. Thank you!

Nikolay [14]

The vertex where the two triangles touch forms a pair of vertical angles, so that the angles on opposites sides of the vertex are congruent. You're shown that two legs of both triangles are congruent. All this tells you that the two triangles are isosceles, and furthermore that they are similar because of the congruence of their "base" angles.

This means

$82^\circ=m\angle 2$