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sattari [20]
3 years ago
7

Write the following sum using summation notation -2/5+3/6-4/7........11/14

Mathematics
1 answer:
horrorfan [7]3 years ago
3 0

Answer:

\sum_{n=1}^{10}(-1)^n\left ( \frac{n+1}{n+4} \right )

Step-by-step explanation:

Given: \frac{-2}{5}+\frac{3}{6}-\frac{4}{7}+...+\frac{11}{14}

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 \sum is called the index of summation.

Let x_1,x_2,x_3,...,x_n denote a set of n numbers.

Then in summation notation,

x_1+x_2+x_3+...+x_n=\sum_{i=1}^{n}x_i

\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 )

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