Arithmatico-geometric series

Algebra Level 4

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


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