Use the approach in Gauss's Problem to find the following sums (do not use formulas)
b. 1 + 3 + 5 + 7 +..... + 1001
Clearly the first number is 1, and last number is 1001, and the increment is 2. This a plug n chug.
yes but, i will have to use a formula that way -
3*+2+2/-2^2
1+3+5+...+2009
To find the sum of the given series 1 + 3 + 5 + 7 + ... + 1001 using Gauss's problem approach, we can follow these steps without using formulas:
1. Find the number of terms in the series:
The series starts with 1 and ends with 1001, and the increment between each term is 2. We can calculate the number of terms using the formula:
Number of terms = (Last term - First term) / Increment + 1
Number of terms = (1001 - 1) / 2 + 1
Number of terms = 1000 / 2 + 1
Number of terms = 500 + 1
Number of terms = 501
2. Find the average of the first and last term:
The average of any arithmetic series can be calculated by adding the first and last term and dividing by 2.
Average = (First term + Last term) / 2
Average = (1 + 1001) / 2
Average = 1002 / 2
Average = 501
3. Multiply the average by the number of terms:
Sum = Average * Number of terms
Sum = 501 * 501
Sum = 251,001
Therefore, the sum of the series 1 + 3 + 5 + 7 + ... + 1001 is 251,001.