Determine how many terms of the following convergent series must be summed to be sure that the remainder is less than 10 Superscript negative 5 in magnitude. Summation from k equals 1 to infinity StartFraction (negative 1 )Superscript k plus 1 Over k cubed EndFraction

You need to sum at least 5000 terms

Step-by-step explanation:

Remember what the estimation theorem for alternating series says.

Given a series

An upper bound for the error of the series  is so

For this case you want

is approximately 5000. So you must sum at least 5000 terms.

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2