SOLUTION: Explain how to find the sum 1+2+3+4+...+175 without using the sum formula.

Question 1178891: Explain how to find the sum 1+2+3+4+...+175 without using the sum formula.
Found 4 solutions by Boreal, Solver92311, math_helper, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
1+175
2+174
3+173
...
87+89
+88
this is 176*87+88=15,400
check with the formula which would be 175*176/2=175*88=15,400

Answer by Solver92311(821)   (Show Source): You can put this solution on YOUR website!

There are several ways:

Add 2 to 1, then add 3 to that sum, then 4 to the previous sum, and so on until you have added 175 to the immediately previous sum. Not a recommended solution.

Add 1 to 175 and write down the sum, namely 176.
Add 2 to 174 and write down the sum, namely 176.
Continue in this fashion until you get to 87 + 89
Count the number of sums of 176 that you have and multiply 176 by that number.
Finally, add 88 to your previous result.

Open a blank Excel spreadsheet.
In cell A1, type the following: =row()
Then press enter
Put the "+" cursor on the lower right corner of cell A1
Hold the left mouse button and drag the mouse down until you have copied the contents of cell A1 into all of the cells from A1 to A175.
In cell A176, type the following: =sum(A1:A175)
Then press enter. The correct sum will appear in cell A176.

Ask someone else to use the sum formula and tell you the answer.

When you are done, ask your instructor what exactly s/he was trying to teach you with this ridiculous exercise.

John

My calculator said it, I believe it, that settles it

From
I > Ø

Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!

Write the sum S both forward and backward:
S = 1 + 2 + 3 + ... + 174 + 175
S = 175 + 174 + 173 + ... + 2 + 1
Add the equations:
2S = 176 + 176 + 176 + ... + 176 + 176
The RHS has 175 terms, re-write it:
2S = 175*176
Solve for S:
S = 175*176/2 = 15400
Answer by ikleyn(52914)   (Show Source): You can put this solution on YOUR website!
.

The sum 1 + 2 + 3 + . . . + n = . The sum 1 + 2 + 3 + . . . + 175 = . Use your calculator.

For introductory lessons on arithmetic progressions see
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
in this site.

You will find there different approaches to calculating similar sums.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

////////////

Your attempts to do it without using the summing formula (which exists in several different incarnations)

recall me the attempts to rotate the history wheel in the opposite direction,

to the before-Karl-Friedrich-Gauss times.

RELATED QUESTIONS
Use the Binomial Theorem to express the following sum in closed form (without using a... (answered by ikleyn)
Please help me solve the following problems. I've tried to solve the problem but I don't (answered by venugopalramana)
how to find the distance between the points using the distance formula? 1) (-4,-20) , (answered by ewatrrr)
Explain how to find the sum -65 + (+41) using a number line, then give the... (answered by CubeyThePenguin)
USING THE GEOMETRIC SUM FORMULA FIND THE SUM OF... (answered by Fombitz)
the formula you use to find the sum of 1-1000 1+2=3+3=6+4=10+5=15 ..... Thank you! (answered by bucky)
Use the geometric sequence of numbers 1, 2, 4, 8,�to find the following: 1. What is r, (answered by longjonsilver)
1) Use the geometric series of numbers 1, 2, 4, 8,�to find the following: a) What is r,... (answered by venugopalramana)
Use the geometric sequence of numbers 1, 2, 4, 8,�to find the following: a)What is r,... (answered by sarah_adam)