Use sigma notation to write the sum $$\frac { 5 } { 1 + 1 } + \frac { 5 } { 1 + 2 } + \frac { 5 } { 1 + 3 } + \cdots + \frac { 5 } { 1 + 22 }$$
A) $\sum _ { j = 1 } ^ { 22 } \frac { 110 } { 22 + j }$
B) $\sum _ { j = 1 } ^ { 5 } \frac { 110 } { j + 22 }$
C) $\sum _ { j = 1 } ^ { 22 } \frac { 5 } { 22 + j }$
D) $\sum _ { j = 1 } ^ { 22 } \frac { 5 } { 1 + j }$
E) $\sum _ { j = 1 } ^ { 22 } \frac { 110 } { 1 + j }$

Question

Use sigma notation to write the sum $$\frac { 5 } { 1 + 1 } + \frac { 5 } { 1 + 2 } + \frac { 5 } { 1 + 3 } + \cdots + \frac { 5 } { 1 + 22 }$$ 
A) $\sum _ { j = 1 } ^ { 22 } \frac { 110 } { 22 + j }$
B) $\sum _ { j = 1 } ^ { 5 } \frac { 110 } { j + 22 }$
C) $\sum _ { j = 1 } ^ { 22 } \frac { 5 } { 22 + j }$
D) $\sum _ { j = 1 } ^ { 22 } \frac { 5 } { 1 + j }$
E) $\sum _ { j = 1 } ^ { 22 } \frac { 110 } { 1 + j }$

Quizplus · Accepted Answer

The given sum can be expressed in sigma notation as the sum from $j = 1$ to $j = 22$ of $\frac{5}{1 + j}$, which matches option D. Each term of the sum has a numerator of 5 and a denominator that starts at 2 (1+1) and increases by 1 for each subsequent term, up to 23 (1+22).

Use Sigma Notation to Write the Sum 51+1+51+2+51+3+⋯+51+22\frac { 5 } { 1 + 1 } + \frac { 5 } { 1 + 2 } + \frac { 5 } { 1 + 3 } + \cdots + \frac { 5 } { 1 + 22 }1+15​+1+25​+1+35​+⋯+1+225​

Use Sigma Notation to Write the Sum $\frac { 5 } { 1 + 1 } + \frac { 5 } { 1 + 2 } + \frac { 5 } { 1 + 3 } + \cdots + \frac { 5 } { 1 + 22 }$