How to Add Consecutive Integers from 1 to

Step-by-Step Guide

1. 1

   Step 1: Write the formula for finding the sum of an arithmetic series.

   The formula is Sn=n(a1+an2){\displaystyle S_{n}=n({\frac {a_{1}+a_{n}}{2}})}, where n{\displaystyle n} equals the number of terms in the series, a1{\displaystyle a_{1}} is the first number in the series, an{\displaystyle a_{n}} is the last number in the series, and Sn{\displaystyle S_{n}} equals the sum of n{\displaystyle n} numbers., This means substituting the first term in the series for a1{\displaystyle a_{1}}, and the last term in the series for an{\displaystyle a_{n}}.
   
   When adding consecutive numbers 1 through 100, a1=1{\displaystyle a_{1}=1} and an=100{\displaystyle a_{n}=100}.
   
   Thus, your formula will look like this:
   S100=n(1+1002){\displaystyle S_{100}=n({\frac {1+100}{2}})}. , Since 100+1=101{\displaystyle 100+1=101}, you will divide 101 by 2: 1012=50.5{\displaystyle {\frac {101}{2}}=50.5}. , This will give you the sum the consecutive number in the series.
   
   In this instance, since you are adding consecutive numbers to 100, n=100{\displaystyle n=100}.
   
   So, you would calculate 100(50.5)=5050{\displaystyle 100(50.5)=5050}.
   
   Thus, the sum of the consecutive numbers between 1 and 100 is 5,050.
   
   To quickly multiply a number by 100, move the decimal point two places to the right.
2. 2

   Step 2: Plug the values into the formula.

3. 3

   Step 3: Add the values in the numerator of the fraction

4. 4

   Step 4: then divide by 2.

5. 5

   Step 5: Multiply by n{\displaystyle n}.

Detailed Guide

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