geometric sequence

Question

1/4+2/4+2²/4+2³/4+...+2^n-1/4

Answer 1

1/4 + 2/4 + 2²/4 + ... = (1/4)[1 + 2 + 2² + 2³ + ...]

 

The expression in the brackets is a geometric series with common ratio

r = 2 (if you divide a term by the term preceding it,  you always get 2).  Since r is not in the interval (-1,1), the series diverges.