the question is:

Show that if

(a(sub 0)/1) + (a(sub 1)/2) +... (a(sub n)/n+1) = 0

then

a(sub 0) + a(sub 1)*x +... a(sub n)*(x^n) = 0

for some x in the interval [0,1]

I have not leaned anything about infinite series, so the solution doesnt pertain to that. I am guessing it has something to do with Sigma notation, and i can transfer the given equations to Sigma notation, but i have no idea where to go from there.

This is my guess at what it is saying in Sigma Notation, but I am not very good with it so I may be wrong

show that if

then

for some x in [0,1]

I need help ASAP! thank you