Express this sum using summation notation: 1 + 3 + 5 + 7 + … + 81.

A) $\sum _ { i = 1 } ^ { 81 } ( 2 i - 1 )$
B) $\sum _ { i = 1 } ^ { 40 } ( 2 i + 1 )$
C) $\sum _ { i = 1 } ^ { 41 } 2 i$
D) $\sum _ { i = 1 } ^ { 41 } ( 2 i - 1 )$
E) $\sum _ { i = 1 } ^ { 81 } ( i + 1 )$

Question

Express this sum using summation notation: 1 + 3 + 5 + 7 + … + 81.

A) $\sum _ { i = 1 } ^ { 81 } ( 2 i - 1 )$
B) $\sum _ { i = 1 } ^ { 40 } ( 2 i + 1 )$
C) $\sum _ { i = 1 } ^ { 41 } 2 i$
D) $\sum _ { i = 1 } ^ { 41 } ( 2 i - 1 )$
E) $\sum _ { i = 1 } ^ { 81 } ( i + 1 )$

Quizplus · Accepted Answer

The series 1, 3, 5, 7, ... 81 represents the sequence of odd numbers. The nth odd number can be represented by the formula $2n - 1$. Since 81 is the 41st odd number, the correct representation using summation notation is $\sum _ { i = 1 } ^ { 41 } ( 2 i - 1 )$.

Express This Sum Using Summation Notation: 1 + 3 ∑i=181(2i−1)\sum _ { i = 1 } ^ { 81 } ( 2 i - 1 )∑i=181​(2i−1)

Express This Sum Using Summation Notation: 1 + 3 $\sum _ { i = 1 } ^ { 81 } ( 2 i - 1 )$