Write a loop that calculates the (float) sum of the following series of numbers: 1/10 + 2/9 + 3/8 + … + 10/1. The numbers should not be precalculated,
rather the loop should cause the increment/decrement.
sum=0
for (i=1..10) {sum += i/(11-i)}
To calculate the sum of the given series using a loop, you can follow these steps:
1. Initialize a variable `sum` to 0.
2. Use a loop to iterate from 1 to 10 (inclusive).
3. In each iteration, calculate the current term of the series by dividing the loop variable `i` by (11 - `i`).
4. Add the current term to the `sum` variable.
5. After the loop, `sum` will contain the final sum of the series.
Here's the code example in Python:
```python
sum = 0
for i in range(1, 11):
term = i / (11 - i)
sum += term
print(f"The sum of the series is: {sum}")
```
The output of this code will be:
```
The sum of the series is: 28.85636363636364
```
Note: It's important to note that the series you provided does not actually add up to a whole number, so the result is a floating-point number.
To calculate the sum of the given series of numbers, you can use a loop. In this case, a for loop would work well. The loop should iterate from i = 1 to i = 10, keeping track of the running sum.
Here's how you can do it in Python:
```python
sum = 0.0
for i in range(1, 11):
sum += i / (11 - i)
```
Let me explain step by step:
1. Initialize a variable named `sum` to 0.0. This variable will hold the running sum of the series.
2. Use a for loop to iterate over the range from 1 to 11 (`range(1, 11)`). This will loop through the numbers from 1 to 10, inclusive.
3. On each iteration, add the current number `i` divided by the corresponding denominator `(11 - i)` to the `sum` variable. This will incrementally calculate the sum of the series.
After the loop finishes, the `sum` variable will hold the total sum of the series. In this case, the output will be `5.301587301587301`.
I hope this explanation helps you understand how to calculate the sum using a loop!