Given that x⟶0, hence 1x≈2x≈3x≈4x≈1 Since all the numbers are tending to the same value, we can take their Geometric Mean in place of Arithmetic Mean. (‌
1x+2x+3x+4x
4
)=(1x2x3x4x)1∕4 And the value of the limit =[(1x2x3x4x)1∕4]1∕x =241∕4=(4!)1∕4