How do you do these two questions?

Step-by-step explanation:

∑ₙ₌₁°° (2x + 3)ⁿ / (n9ⁿ)

Use ratio test:

lim(n→∞)│aₙ₊₁ / aₙ│< 1

lim(n→∞)│[(2x + 3)ⁿ⁺¹ / ((n+1) 9ⁿ⁺¹)] / [(2x + 3)ⁿ / (n9ⁿ)]│< 1

lim(n→∞)│(2x + 3) n / (9 (n+1))│< 1

│(2x + 3) / 9│< 1

│2x + 3│< 9

-9 < 2x + 3 < 9

-12 < 2x < 6

-6 < x < 3

If x = -6, ∑ₙ₌₁°° (2(-6) + 3)ⁿ / (n9ⁿ) = ∑ₙ₌₁°° (-1)ⁿ / n, which converges.

If x = 3, ∑ₙ₌₁°° (2(3) + 3)ⁿ / (n9ⁿ) = ∑ₙ₌₁°° 1 / n, which diverges.

The interval of convergence is therefore [6, 3).

∑ₙ₌₁°° (x + 4)ⁿ / n!

Use ratio test:

lim(n→∞)│aₙ₊₁ / aₙ│< 1

lim(n→∞)│[(x + 4)ⁿ⁺¹ / (n+1)!] / [(x + 4)ⁿ / n!]│< 1

lim(n→∞)│(x + 4) n! / (n+1)!│< 1

lim(n→∞)│(x + 4) / (n + 1)│< 1

0 < 1

The interval of convergence is therefore (-∞, ∞).

a framing bias

step-by-step explanation:

rodrigo is subject to a framing bias i believe.

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form