Respuesta :

S=1+5+5²+5³+5⁴
5S=5+5²+5³+5⁴+5⁵
5S-S=4S=5⁵-1
The expression is 5⁵-1 (=3124)

Answer:

The given series is written in expression form as [tex]\sum _{n=0}^4\:5^n[/tex]

Step-by-step explanation:

Given : series 1+5+25+125+625

We have to find the expression  for the given series 1+5+25+125+625

Consider the given series 1+5+25+125+625

1 can be written as [tex]5^0[/tex]

5 can be written as [tex]5^1[/tex]

25 can be written as [tex]5^2[/tex]

125 can be written as [tex]5^3[/tex]

625 can be written as [tex]5^4[/tex]

Thus, the general representation of the series is [tex]5^n[/tex] for n is 0 to 4.

Thus,  The given series is written in expression form as [tex]\sum _{n=0}^4\:5^n[/tex]