How do you do this question?

9 · 2⁹

(-½, ½)

Step-by-step explanation:

The nth term of the original power series is 2ⁿ xⁿ.

Therefore, the nth term of the derived power series is:

d/dx (2ⁿ xⁿ) = n · 2ⁿ xⁿ⁻¹

When n=9, the term is 9 · 2⁹ x⁸.

Use ratio test:

lim(n→∞)│aₙ₊₁ / aₙ│

lim(n→∞)│((n+1) · 2ⁿ⁺¹ xⁿ) / (n · 2ⁿ xⁿ⁻¹)│

lim(n→∞)│(n+1) · 2x / n│

2│x│

The series converges when the limit is less than 1.

2│x│< 1

│x│< ½

-½ < x < ½

Check the endpoints.

If x = -½, the series is ∑ n · 2ⁿ (-½)ⁿ⁻¹ = ∑ -2n · (-1)ⁿ, which diverges.

If x = ½, the series is ∑ n · 2ⁿ (½)ⁿ⁻¹ = ∑ 2n, which diverges.

So the interval of convergence is (-½, ½).

50*10 is greater

step-by-step explanation:

if you add the zero from 10 to 50, it will give you a bigger number.

the answer is 9.8975

explanation:

when you multiply the "39.59" with the 25% it reduces it and shows its final discounted price. hope this !

step-by-step explanation: