O4440 O4440
  • 01-12-2019
  • Mathematics
contestada

does this sum converge: show steps

does this sum converge show steps class=

Respuesta :

MathPhys
MathPhys MathPhys
  • 01-12-2019

Answer:

Yes

Step-by-step explanation:

[tex]\sum_{n=1}^{\infty} e^{-\sqrt{n} } \\\sum_{n=1}^{\infty} (\frac{1}{e})^{\sqrt{n} }[/tex]

If we say u = √n, then:

[tex]\sum_{u=1}^{\infty} (\frac{1}{e})^{u}[/tex]

This is a geometric series.  Since |1/e| < 1, the series converges.

Answer Link

Otras preguntas

what is a newton equal to in terms of mass and acceleration
Which nuclides are used to date the remains of a once-living organism? (1) C-14 and C-12 (3) I-131 and Xe-131 (2) Co-60 and Co-59 (4) U-238 and Pb-206
Factor 8x2 + 12x – 3. A. (2x – 1)(4x + 3) B. (2x + 3)(4x – 1) C. (8x + 1)(x – 3) D. The polynomial is prime.
a sphere is circumscribed about an 8-inch by 8-inch by 8-inch cube. Find the volume to the nearest cubic inch.
75 students decreased by 80%
What is the molarity of 1.5 liters of an aqueous solution that contains 52 grams of lithium fluoride, LiF, (gram-formula mass =26 grams/mole)? (1) 1.3 M (3) 3.0
How did feudalism help the people of the Middle Ages deal with outside threats like barbarians, famine, and war? Select the best answer from the choices provide
a sphere is circumscribed about an 8-inch by 8-inch by 8-inch cube. Find the volume to the nearest cubic inch.
Who rejected US membership in the League of Nations and ultimately the Treaty of Versailles a. Allied leaders b. The US Senate c. President Wilson d. The House
im what direction does heat flow or transfer?