Question

Which expression represents the series 1+5+25+125+625

Answer 1

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

Answer 2

The given series is written in expression form as
`\sum _(n=0)^4\:5^n`

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
`5^0`

5 can be written as
`5^1`

25 can be written as
`5^2`

125 can be written as
`5^3`

625 can be written as
`5^4`

Thus, the general representation of the series is
`5^n` for n is 0 to 4.

Thus, The given series is written in expression form as
`\sum _(n=0)^4\:5^n`