### Use definition to show that sequence is Cauchy.

Use the definition to show that the sequence (n-1)/(n+2) (n=1 to infinity) is Cauchy. Please show all steps.

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Use the definition to show that the sequence (n-1)/(n+2) (n=1 to infinity) is Cauchy. Please show all steps.

See attached file for full problem description. Use the definition of convergence of a sequence to prove that the sequence (n-1)/(n+2) (n=1 to infinity) converges to 1. Please provide complete proof and explanation.

State the definition of a Cauchy sequence. Also, by negating this definition, state the definition of a sequence to be not Cauchy.

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0=-3,000 + 2500/(1+r)+ 1000/(1+r)^2 r=

The surface area of a right circular cylinder is given by the formula... (see attachment)

The surface area of a right circular cylinder is given by the formula S= 2*PIE SIGN*rh + 2*PIE SIGN* r^2, where r is the radius of the base, and h is the height of the cylinder. Solve the formula S= 2*PI*rh + 2*PI*r^2 for h.

Although Corollary 2 does not apply to the function 1 / (z — z_0) in the plane punctured at z_0, Theorem 6 can be used as follows to show that (see attached 1) for any circle C traversed once in the positive direction surrounding the point z_0. Introduce a horizontal branch cut from z_0 to infinity as in Fig. 4.25. In the r

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Below problem is one that I'm drawing a blank on for even setting up the equation. Any help would be greatly appreciated. Smith recently inherited a large sum of money; he wants to use a portion of this money to set up a trust fund for his two children. The trust fund has two investment options: (1) a bond fund and (2) a st

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Solve the following equation by completing the square. See Attached for equation

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Solve for y. Watch for extraneous solutions. See attachment for equation