series Question

[bhdeepak]

Ron,Stacey,Other MGMAT instructors
would appreciate help in solving the following question

if x=-1 and n is the sum of first 4 prime numbers what is 1+x+x^n +x^(n+1)+x^(n+2)+....

Thanks in advance

[rajkapoor]

bhdeepak,

i am going to give it a try

x = (-1)

n = 14 ( 2 + 3 + 4 + 5)

the equation reduces to

Sum = 1 -1 +(-1)^14 + (-1)^15 +....x^(n+n)+x^(2n+1)....
Sum = 1-1+1-1+......+(-1)^2n + (-1)^2n+1.....

Sum = 0 if the exponent in last number of the sequence is odd
and will be 1 if the exponent in last number of the sequence is even.

[sunil_snath]

Hi Raj,

I think n=17.

n is the sum of the first 4 PRIME numbers,

so n = 2+3+5+7 = 17

So going by the same method,

Sum = 0 if the exponent in last number of the sequence is even
and will be -1 if the exponent in last number of the sequence is odd.

[rajkapoor]

yep - you are right / n = 17



- raj

[RonPurewal]

Hi Raj,

I think n=17.

n is the sum of the first 4 PRIME numbers,

so n = 2+3+5+7 = 17

So going by the same method,

Sum = 0 if the exponent in last number of the sequence is even
and will be -1 if the exponent in last number of the sequence is odd.

this is accurate.

did the original problem statement indicate the point at which the series stops?
if not, there's actually no answer to the problem -- you can't assign a value to an infinite sum that oscillates forever between two numbers.

what's the source of the problem? actually, we'll have to delete this thread in the next couple of weeks if you don't cite the source.

[bhdeepak]

Ron,

this problem is from actual GMAT exam.