If n is a positive integer, then lim n→∞ 1/n[(1/n)^2+(2/n)^2++((n-1)/n)^2] can be expressed

safety professionals realize that high-dexterity gloves result in increased safety and job performance. corporate managers know that increased safety reduces costs while increased performance enhances productivity, both of which boost the bottom line. that being said, why do we still see so many work sites where gloves are not mandated ppe or where gloves are mandated but compliance falls short of expectations? after all, the most important tools for every employee are his brains, eyes, and hands--he can't work without all three of them functioning properly.

hard hats and safety glasses top the list of required ppe at most work sites, but gloves fall to a distant third or fourth. and even when gloves are mandated, they're often found on the ground more than on employees' hands. why is that?

the reason is that lack of hand dexterity has historically made gloves too cumbersome to work in. if an employee can't adequately control the tools he or she is working with--if he can't feel the details of the metal pipe, wood beam, parcel package, machine screw, airplane wing, concrete block, pine log, steel girder, or engine part that he's handling--then the gloves themselves pose an even higher risk of injury than not wearing any gloves at all.

the lack of mandated hand protection (and the lack of compliance when it is mandated) is a direct result of traditional gloves' preventing workers from effectively and safely performing their jobs. if linda's gloves are too cumbersome to allow her to position a set of steel springs with one hand and pneumatically staple them to a mattress frame with the other hand, she's just not going to wear them. can you blame her?

in a nutshell, the lack of dexterity in gloves has prevented them from becoming universally required and accepted hand protection. and that's a sad thing, because no matter how talented you are at the job you perform, you can't work with injured hands.