Write the first five terms of the sequence of partial sums. $$5 + \frac { 5 } { 4 } + \frac { 5 } { 9 } + \frac { 5 } { 16 } + \frac { 5 } { 25 } + \cdots$$
A) $5 , \frac { 5 } { 4 } , \frac { 5 } { 9 } , \frac { 5 } { 16 } , \frac { 1 } { 5 }$
B) $5 , \frac { 5 } { 2 } , \frac { 225 } { 32 } , \frac { 250 } { 33 } , \frac { 525 } { 64 }$
C) $5 , \frac { 25 } { 6 } , \frac { 245 } { 32 } , \frac { 1025 } { 132 } , \frac { 5269 } { 640 }$
D) $5 , \frac { 35 } { 4 } , \frac { 275 } { 36 } , \frac { 1075 } { 144 } , \frac { 265 } { 36 }$
E) $5 , \frac { 25 } { 4 } , \frac { 245 } { 36 } , \frac { 1025 } { 144 } , \frac { 5269 } { 720 }$

Question

Quizplus · Accepted Answer

The sequence of partial sums is obtained by adding each term to the sum of all previous terms. The first term is 5. The second term is $5 + \frac{5}{4} = \frac{25}{4}$. The third term is $\frac{25}{4} + \frac{5}{9} = \frac{245}{36}$. The fourth term is $\frac{245}{36} + \frac{5}{16} = \frac{1025}{144}$. The fifth term is $\frac{1025}{144} + \frac{5}{25} = \frac{5269}{720}$.

Write the First Five Terms of the Sequence of Partial 5+54+59+516+525+⋯5 + \frac { 5 } { 4 } + \frac { 5 } { 9 } + \frac { 5 } { 16 } + \frac { 5 } { 25 } + \cdots5+45​+95​+165​+255​+⋯

Write the First Five Terms of the Sequence of Partial $5 + \frac { 5 } { 4 } + \frac { 5 } { 9 } + \frac { 5 } { 16 } + \frac { 5 } { 25 } + \cdots$