BUILT-IN MATHEMATICA SYMBOL

NProduct

NProduct[f, {i, i_min, i_max}]
gives a numerical approximation to the product .

NProduct[f, {i, i_min, i_max, di}]
uses a step di in the product.

Details and Options Details and Options

NProduct can be used for products with both finite and infinite limits.
NProduct[f, {i, ...}, {j, ...}, ...] can be used to evaluate multidimensional products.
The following options can be given:

AccuracyGoal	Infinity	number of digits of final accuracy sought
EvaluationMonitor	None	expression to evaluate whenever f is evaluated
Method	Automatic	method to use
PrecisionGoal	Automatic	number of digits of final precision sought
VerifyConvergence	True	whether to explicitly test for convergence
WorkingPrecision	MachinePrecision	the precision used in internal computations

Possible settings for the Method option include:
"EulerMaclaurin" Euler-Maclaurin summation method

"WynnEpsilon" Wynn epsilon extrapolation method
With the Euler-Maclaurin method, the options AccuracyGoal and PrecisionGoal can be used to specify the accuracy and precision to try and get in the final answer. NProduct stops when the error estimates it gets imply that either the accuracy or precision sought has been reached.
You should realize that in sufficiently pathological cases, the algorithms used by NProduct can give wrong answers. In most cases, you can test the answer by looking at its sensitivity to changes in the setting of options for NProduct.
VerifyConvergence is only used for products with infinite limits.
N[Product[...]] calls NProduct.
NProduct first localizes the values of all variables, then evaluates f with the variables being symbolic, and then repeatedly evaluates the result numerically.
NProduct has attribute HoldAll, and effectively uses Block to localize variables.