Determine which series is convergent.
A)
$- \frac { 2 } { 7 } + \frac { 3 } { 8 } - \frac { 4 } { 9 } + \frac { 5 } { 10 } - \frac { 6 } { 11 } - \ldots$
B)
$\frac { 4 } { 3 } - \frac { 4 } { 4 } + \frac { 4 } { 5 } - \frac { 4 } { 6 } + \frac { 4 } { 7 } - \ldots$

Question

Determine which series is convergent. 
A)
$- \frac { 2 } { 7 } + \frac { 3 } { 8 } - \frac { 4 } { 9 } + \frac { 5 } { 10 } - \frac { 6 } { 11 } - \ldots$
B)
$\frac { 4 } { 3 } - \frac { 4 } { 4 } + \frac { 4 } { 5 } - \frac { 4 } { 6 } + \frac { 4 } { 7 } - \ldots$

Quizplus · Accepted Answer

Both series are alternating series, but B has a constant numerator and increasing denominator, which means it satisfies the conditions for the alternating series test (the terms converge to zero and are decreasing in magnitude). Therefore, series B is convergent. Series A is also alternating, but the numerator increases and the denominator increases faster, which does not satisfy the alternating series test.

Determine Which Series Is Convergent −27+38−49+510−611−…- \frac { 2 } { 7 } + \frac { 3 } { 8 } - \frac { 4 } { 9 } + \frac { 5 } { 10 } - \frac { 6 } { 11 } - \ldots−72​+83​−94​+105​−116​−…

Determine Which Series Is Convergent $- \frac { 2 } { 7 } + \frac { 3 } { 8 } - \frac { 4 } { 9 } + \frac { 5 } { 10 } - \frac { 6 } { 11 } - \ldots$