The left side is  .


The right side is   =  = .


Then, comparing the left and the right sides, you get several solutions in integer numbers:


    n = 12,  x =  = 125,

    n = 11,  x       = 250,

    n = 10,  x       = 500,

    n =  9,  x       = 1000,

    n =  8,  x       = 2000,
      
    n =  7,  x       = 4000,

    . . . .  and so on . . .  


    n =  0,  x        = .

Equating terms, we can say that: , which results in: 

The right side can also be SIMPLIFIED to: 

Either of the 2 works!!

That's it!! 

RELATED QUESTIONS

Given the functions f(n)=500 and g(n)= (9/10)^n-1, combine them to create a geometric... (answered by ewatrrr)

solve for n:  n=... (answered by jim_thompson5910)

solve for n: n=... (answered by jim_thompson5910,josmiceli)

A regular polygon has n equal sides and n equal angles. The measure a of an interior... (answered by Tatiana_Stebko)

Solve the given equation for n 6(n+6)=2... (answered by Fombitz)

i need to solve this problem for x.

log x^1/2 = sq rt (log x)

and 

for equation... (answered by solver91311)

Given the functions f(n) = 500 and g(n) = ()n − 1, combine them to create a... (answered by richwmiller)

Solve the equation for the value of n: {{{x^(n-1)+x^(n+1)=320}}}

My approach was 


 (answered by ikleyn)

Can you explain how to to solve this problem? 
n=x
  ∑    = n^2-2n+1=630
n=12... (answered by stanbon)