Note that the following series is telescoping. If it is convergent, compute its

Question

Note that the following series is telescoping. If it is convergent, compute its sum. Otherwise, enter DIV .

Determine the sum of the following series:

Using partial fractions, Determine whether the following telescoping series is convergent or divergent. If convergent find the sum, and if divergent enter DIV: 8/n(n+1) If the nth partial sum of a series Find the values of x for which the series xn / 4n converges. Find the sum of the series for those values of x. Express 10.6364.. . as a rational number, in the form p/q here p and q are positive integers with no common factors (3n+5n/9n)= (0.3 n-1 - 0.9n)=

Explanation / Answer

(a)

A = 3.5, B = -3.5

(b)

convergent

sum = 21/4 = 5.25

(c)

convergent sum = 8

(d)

an = 12/(n^2 +7n +12)

sum = 1

(a)

-4<x<4

(b)

sum = x/(4-x)

(c)

sum = 1/2 + 5/4 = 7/4 = 1.75

sum = 1/0.7 -0.9/0.1 = 10/7-9 = -53/9

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