# Arithmatico-geometric series

**Algebra**Level 4

The *n*th term of an infinite series is given by:-
\[t_n = nx^{n-1},\]
Where \(t_n\) represents the *n*th term

And it is given that:-
\[\sum_{n=1}^{\infty} nx^{n-1} = 4, \]
Where x is a real number lying between 0 and 1.

Calculate the value of x.

Note:-Since numbers being added are infinite so sum of above sequance is not actualy 4, if **t n**

*denotes _n*th term of above series and

**S**denotes sum of n terms of this series then then

**4**is the limit of

**S**when

**n**approach to infinity