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

PLEASE HELP ME 20 POINTS Some metals have a molecular structure that makes them good conductors. Explain how understanding this relationship can help engineers
evaluate :5+1/6(-5/3)​
Simplify7⁸×7³×7⁴÷7⁹×7⁵​
2 over 5 divided by 6 over 7
a person sold a house for Tzs 475 and incurred a loss of 5%.at what price would it been sold so as to earn a profit of 8%​
The Second Great Awakening: a) focused on reforming Southern social structure. b) encouraged people to persecute Mormons. c) led to many reform movements thr
What religion did King Ashoka adopt? 1.Buddhist 2.Hindu 3.Christian 4.Jewish
if y varies directly with x and y is 12 when x is 9 what is x when y is 4
The structures common to all protozoa are?
What are m and b in the linear equation 12 + 6x + 15 + 10x = y?