SOLUTION: Express as a fraction in simplest form: 8+16+24+…+784/6+12+18+…+588

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Express as a fraction in simplest form: 8+16+24+…+784/6+12+18+…+588      Log On


   

Question 1185156: Express as a fraction in simplest form:
8+16+24+…+784/6+12+18+…+588
Found 3 solutions by MathLover1, ikleyn, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Express as a fraction in simplest form:
8%2B16%2B24+…+784/6%2B12%2B18+…+588

numerator is:
8%2B16%2B24+…+784-> find nth term formula
a%5Bn%5D=8%2B8%28n-1%29
a%5Bn%5D=8%2B8n-8
a%5Bn%5D=8n
last term is 784, so n is
784=8n
n=784%2F8
n=98
denominator is:
6%2B12%2B18+…+588
a%5Bn%5D=6%2B6%28n-1%29
a%5Bn%5D=6%2B6n-6
a%5Bn%5D=6n
last term is 588, so+n is
588=6n
n=98-> there are 98 terms in both numerator and denominator

then sum of each sequence is:
sum%288n%2C+n=1%2C98%29=+38808
sum%28+6n%2Cn=1%2C98%29+=+29106
finally, you have
38808%2F29106=4%2F3

Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.


            Actually,  it is a joke problem,  and in my post below  I  will explain you  WHY. 


The numerator is


    8 + 16 + 24 + . . . + 784 = 8*(1 + 2 + 3 + . . . 98).


The denominator is


    6 + 12 + 18 + . . . + 588 = 6*(1 + 2 + 3 + . . . 98).


When you take the fraction, the sums in parentheses will cancel each other - - - so THERE IS NO NEED to calculate them.


The final answer is  8%2F6 = 4%2F3.


        If you will solve it following the  @MathLover1 post,  there is a risk that people will laugh at you.



Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Note first of all that your expression is not shown correctly; parentheses are required.

"(8+16+24+…+784)/(6+12+18+…+588)", not just "8+16+24+…+784/6+12+18+…+588"

Take a few seconds to note that the numerator is

8+16+24+…+784 = 8(1+2+3+...+98)

and the denominator is

6+12+18+…+588 = 6(1+2+3+...+98)

Simplifying the fraction is then simple:

(6(1+2+3+...+98))/(8(1+2+3+...+98)) = 6/8 = 3/4

ANSWER: 3/4