Best solutions to - "Solving summation problem∑i=x2x5−∑k=2x+15x+25=−25"

Jaylin Clements

Answered question

2022-03-31

Solving summation problem

\sum_{i = x}^{2 x} 5 - \sum_{k = 2 x + 1}^{5 x + 2} 5 = - 25

allemelrypi0e

Beginner2022-04-01Added 11 answers

Here we need to count how many integers there are between x and 2x and between

2 x + 1

and

5 x + 2

. Since you are not familiar with these things, try to write all possible numbers. You'll get something like

x, x + 1, \dots, x + (x - 1), 2 x

and

2 x + 1, \dots, 2 x + (x - 1), 3 x, 3 x + 1, \dots, 3 x + (x - 1), 4 x, 4 x + 1, \dots, 4 x + (x - 1), 5 x, 5 x + 1, 5 x + 2

Now it's easy to see that you have

x + 1

numbers between x and 2x and

3 x + 2

between

2 x + 1

and

5 x + 2

Theodore Davila

Beginner2022-04-02Added 14 answers

Use the fact that

\sum_{i = x}^{2 x} 5 = 5 \cdot (2 x - x) = 5 x

and

\sum_{k = 2 x + 1}^{5 x + 1} 5 = 5 \cdot (5 x + 1 - 2 x - 1) = 15 x

Then, the equation becomes

5 x - 15 x = - 25

which is easy to solve, you just get

x = \frac{25}{10}

or in simpler terms

x = \frac{5}{2}

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