Докажите равенство ∑n=199991(n+n+1)(n4+n+14)=9.\sum\limits_{n = 1}^{9999} {\dfrac{1}{{\left( {\sqrt n + \sqrt {n + 1} } \right)\left( {\sqrt[4]{n} + \sqrt[4]{{n + 1}}} \right)}} = 9} .n=1∑9999(n+n+1)(4n+4n+1)1=9.