The value of $1+2+3+....+10-50$ is

Question

Accepted Answer

To find the value of $1+2+3+....+10-50$, we first need to calculate the sum of the series $1+2+3+....+10$.

**Step 1: Calculate the sum of the first 10 natural numbers.**
The sum of the first 'n' natural numbers can be found using the formula: $S_n = n(n+1)/2$.
In this case, n = 10.
So, the sum $1+2+3+....+10 = 10(10+1)/2 = 10(11)/2 = 110/2 = 55$.

**Step 2: Subtract 50 from the calculated sum.**
The expression is $ (1+2+3+....+10) - 50 $.
Substituting the sum we found: $ 55 - 50 $.

**Step 3: Perform the subtraction.**
$ 55 - 50 = 5 $.

Therefore, the value of $1+2+3+....+10-50$ is 5.

**Justification for Option 2 (5):**
As calculated in the steps above, the sum of the series $1+2+3+....+10$ is 55. When 50 is subtracted from this sum, the result is $55 - 50 = 5$. This matches Option 2.

**Explanation for why other options are incorrect:**
*   **Option 1 (4):** This option is incorrect because the correct calculation $55 - 50$ yields 5, not 4.
*   **Option 3 (10):** This option is incorrect because the correct calculation $55 - 50$ yields 5, not 10.
*   **Option 4 (55):** This option represents only the sum of the series $1+2+3+....+10$. The question requires subtracting 50 from this sum, so 55 is an intermediate step, not the final answer. The final answer must account for the subtraction of 50.