Q13/096) Find sum of n terms ---- 1 + ( 1 + x ) + ( 1 + x + x² ) + ( 1 + x + x² + x³ ) + ..... + up to nth term.?

y = 1 + (1+ x) + (1+ x + x^2) + ...
y ( 1-x) = (1-x) + 1(1-x^2) + .. ( 1- x^(n))
= n - ( x + x^2 + .. x^(n)) as
= n - x ( 1 + x ... x^(n-1))
= n - x ( 1- x^(n))/(1-x)

or y = n/(1-x) - x (1-x^(n)/(1-x)^2

the above ans is correct if x is not 1

if x = 1 then we have 1 + 2 + 3 + .. n = n(n+1)/2