Respuesta :
Answer:
[tex]\sum_{n=1}^{10}(-1)^n\left ( \frac{n+1}{n+4} \right )[/tex]
Step-by-step explanation:
Given: [tex]\frac{-2}{5}+\frac{3}{6}-\frac{4}{7}+...+\frac{11}{14}[/tex]
To write: the given expression using summation notation
Solution:
Summation notation helps to write a long sum as a single expression.
In the summation notation, the variable [tex]\sum[/tex] is called the index of summation.
Let [tex]x_1,x_2,x_3,...,x_n[/tex] denote a set of n numbers.
Then in summation notation,
[tex]x_1+x_2+x_3+...+x_n=\sum_{i=1}^{n}x_i[/tex]
[tex]\frac{-2}{5}=(-1)^1\left ( \frac{1+1}{1+4} \right )\\\frac{3}{6}=(-1)^2\left ( \frac{2+1}{2+4} \right )\\\frac{-4}{7}=(-1)^3\left ( \frac{3+1}{3+4} \right )\\.\\.\\.\\\frac{11}{14}=(-1)^10\left ( \frac{10+1}{10+4} \right )\\\therefore \frac{-2}{5}+\frac{3}{6}-\frac{4}{7}+...+\frac{11}{14}=\sum_{n=1}^{10}(-1)^n\left ( \frac{n+1}{n+4} \right )[/tex]
