Find the first and third partial sums, s1 and s3, for the sequence
-$$a _ { n } = \frac { n } { n + 2 }$$
A) $\frac { 1 } { 3 } , \frac { 43 } { 30 }$
B) $\frac { 1 } { 3 } , \frac { 1 } { 10 }$
C) $\frac { 1 } { 3 } , \frac { 3 } { 4 }$
D) $\frac { 1 } { 3 } , \frac { 3 } { 5 }$

Question

Quizplus · Accepted Answer

The first partial sum $s_1$ is simply the first term of the sequence, which is $a_1 = \frac{1}{1+2} = \frac{1}{3}$. The third partial sum $s_3$ is the sum of the first three terms: $a_1 + a_2 + a_3 = \frac{1}{3} + \frac{2}{4} + \frac{3}{5} = \frac{1}{3} + \frac{1}{2} + \frac{3}{5} = \frac{10}{30} + \frac{15}{30} + \frac{18}{30} = \frac{43}{30}$.

Find the First and Third Partial Sums, S1 and S3 an=nn+2a _ { n } = \frac { n } { n + 2 }an​=n+2n​

Find the First and Third Partial Sums, S1 and S3 $a _ { n } = \frac { n } { n + 2 }$