How to Add a Consecutive Series of Numbers in Your Head

Step-by-Step Guide

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   Step 1: Imagine the numbers.

   Let's suppose that you want to add all the numbers from 1 to 100 in your head.
   
   Imagine that on a table in front of you you have arranged stacks of pennies, in a long neat row left to right, to equal each of these numbers.
   
   For example, the first stack of pennies starting on the left side of the table is just one penny by itself.
   
   Beside it, to its right is a stack of 2 pennies.
   
   To the immediate right of the 2 penny stack is a stack of 3 pennies, and so on, clear up to a stack that is 100 pennies tall.
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   Step 2: Count the stacks: You have 100

   , You would have a stack that totaled 101 pennies. , You would now have another stack of pennies that totaled 101 pennies! ,, You will always end up with a new stack that totals 101 pennies. ,, We know that if you multiply any number by 100, you just add 2 zeros, so 50 times 100 would be
   5000. ,, Admittedly, it could get rather hard if the series of numbers aren't in well-rounded chunks of numbers, or if they get too large, but this skill can stand you in good stead in daily life, as it can help your estimating skills, and help keep your mind sharp.
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   Step 3: right?

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   Step 4: Imagine what would happen' if you took the penny from stack #1

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   Step 5: and put it on the top of stack #100?

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   Step 6: Imagine if you then took the 2 pennies from stack #2 and put them on top of stack #99 (which has 99 pennies in it)?

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   Step 7: Continue with this pattern by putting the 3 pennies from stack #3 on top of stack #98

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   Step 8: you will see that this also gives you another stack totaling 101 pennies.

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   Step 9: Apply this pattern all the way through

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    Step 10: and it will hold true for each combination of the stack from the right added to the next stack form the left.

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    Step 11: Combine the stacks in this manner

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    Step 12: in your imagination

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    Step 13: until you end up with only 50 stacks

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    Step 14: and each stack now contains 101 pennies.

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    Step 15: Quickly add in your head how many pennies you have by counting the stacks of 101 pennies: 101 times 50.

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    Step 16: Since we are multiplying by 101

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    Step 17: not 100

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    Step 18: you just need to add another 50 to the 5000

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    Step 19: and you come up with the correct total of 5050.

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    Step 20: Use this mental formula to add any series of sequential numbers.

Detailed Guide

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