# numerical methods – Upper bound relative error in IEEE 754 standard

Prove $$∑^{∞}_{i=t} 2^{−i} < 2^{1−t}$$ and show the upper bound for relative error on rounding is
$$2^{-t}$$when t is the number of bits used to represent the mantissa in IEEE 754 standard.

I think it can be proved with geometric progression. However, I’ve no clue how to approach the rest of the problem.