I Question about the derivative of this sum and where n starts

[Frankenstein19]

Ok so when differentiating

1/(1-x)= Σ xⁿ from n=0 to infinity

the book says it is 1/(1-x)^2 = Σ n*(x)^n-1 from n=1 to infinity

i don't understand why the original sum starts at 0 and then the derived sum starts at 1

 

[fresh_42]

Both start with the number 1. If you like you may start the second series at 0, too. It doesn't make a difference because $0 \cdot x^{-1} = 0.$ However, in this case one unnecessarily gets into trouble with $x=0.$

 

[Simon Bridge]

Expand the sum and take the derivative and then rewrite the result in sum notation.

 

[rahul_26]

both starts with 1 because when you put $n=0$ in first series,the answer will be $x^0=1$