# Fragmented timeframes

As the weight accumulates, when a user decides to claim their rewards, we can extract it from the weight.

Where DPS = Distribute per second, US = User Stake, TS = Total Network Stake, UR = User Reward, and n = Time in seconds

$UR1 = (DPS1 * US1 / TS1) + (DPS2 * US1 / TS2) + (DPSn * US1 / TSn)$

We can calculate the user reward within a timeframe, as a to b where b > a

Where n = 1 to a,

$UR1 = US * ∑DPSn / TSn$
$UR = US1 * (DPS1 / TS1 + DPS2 / TS2 + DPSx / TSx)$

Where n = 1 to b,

$UR2 = US * ∑DPSn / TSn$

When a user initiates an action in the network, where a = n > 1, we calculate n from 1 to a. When the same user initiates an action again, we calculate from 1 to b, and subtract the previous 1 to a. This can be represented as :

$UR = US * ∑ DPSn / TSn, (n = 1 : ∞)$

A user's reward between timeframe a and b can be calculated accurately as:

$URab = UR2 - UR1 = (US * ∑DPSn / TSn)$

where n = 1 to b, and

$- (US * ∑DPSn / TSn)$

where n = 1 to a

$= US * ((∑DPSn / TSn, (n=1:b)) - (∑DPSn / TSn, (n = 1:a)))$