\(\frac{a_{1}+\sqrt{a_{1}a_{2}}+\sqrt[3]{a_{1}a_{2}a_{3}}}{a_{1}+a_{2}+a_{3}}

王守恩

\(\frac{a_{1}}{a_{1}}=1.00000\)

\(\frac{a_{1}+\sqrt{a_{1}a_{2}}}{a_{1}+a_{2}}=1.20711\)

\(\frac{a_{1}+\sqrt{a_{1}a_{2}}+\sqrt[3]{a_{1}a_{2}a_{3}}}{a_{1}+a_{2}+a_{3}}=1.33333\)

\(\frac{a_{1}+\sqrt{a_{1}a_{2}}+\sqrt[3]{a_{1}a_{2}a_{3}}+\sqrt[4]{a_{1}a_{2}a_{3}a_{4}}}{a_{1}+a_{2}+a_{3}+a_{4}}=1.42084\)

\(\frac{a_{1}+\sqrt{a_{1}a_{2}}+\sqrt[3]{a_{1}a_{2}a_{3}}+\sqrt[4]{a_{1}a_{2}a_{3}a_{4}}+\sqrt[5]{a_{1}a_{2}a_{3}a_{4}a_{5}}}{a_{1}+a_{2}+a_{3}+a_{4}+a_{5}}= 1.48635\)

\(\frac{a_{1}+\sqrt{a_{1}a_{2}}+\sqrt[3]{a_{1}a_{2}a_{3}}+\sqrt[4]{a_{1}a_{2}a_{3}a_{4}}+\sqrt[5]{a_{1}a_{2}a_{3}a_{4}a_{5}}+\cdots}{a_{1}+a_{2}+a_{3}+a_{4}+a_{5}+\cdots}=?\)

王守恩

就是不知道？？= ？？？——好玩！肯定是一个好玩的数字！！好玩！！！

{02, 1.20711}, {03, 1.33333}, {04, 1.42084}, {05, 1.48635}, {06, 1.53794}, {07, 1.58004}, {08, 1.61532}, {09, 1.64551}, {10, 1.67176}, {11, 1.69489}, {12, 1.71550},
{13, 1.73403}, {14, 1.75083}, {15, 1.76616}, {16, 1.78023}, {17, 1.79321}, {18, 1.80525}, {19, 1.81645}, {20, 1.82692}, {21, 1.83674}, {22, 1.84597}, {23, 1.85468},
{24, 1.86291}, {25, 1.87070}, {26, 1.87811}, {27, 1.88515}, {28, 1.89187}, {29, 1.89828}, {30, 1.90441}, {31, 1.91029}, {32, 1.91592}, {33, 1.92133}, {34, 1.92653},
{35, 1.93154}, {36, 1.93636}, {37, 1.94102}, {38, 1.94552}, {39, 1.94986}, {40, 1.95406}, {41, 1.95813}, {42, 1.96208}, {43, 1.96590}, {44, 1.96961}, {45, 1.97321},
{46, 1.97671}, {47, 1.98012}, {48, 1.98343}, {49, 1.98665}, {50, 1.98979}, {51, 1.99285}, {52, 1.99584}, {53, 1.99874}, {54, 2.00158}, {55, 2.00436}, {56, 2.00707},
{57, 2.00971}, {58, 2.01230}, {59, 2.01483}, {60, 2.01731}, {61, 2.01973}, {62, 2.02210}, {63, 2.02442}, {64, 2.02670}, {65, 2.02893}, {66, 2.03112}, {67, 2.03326},
{68, 2.03537}, {69, 2.03743}, {70, 2.03946}, {71, 2.04145}, {72, 2.04340}, {73, 2.04532}, {74, 2.04721}, {75, 2.04906}, {76, 2.05088}, {77, 2.05267}, {78, 2.05443},
{79, 2.05616}, {80, 2.05787}, {81, 2.05955}, {82, 2.06120}, {83, 2.06282}, {84, 2.06442}, {85, 2.06600}, {86, 2.06754}, {87, 2.06908}, {88, 2.07058}, {89, 2.07207},
{90, 2.07353}, {91, 2.07497}, {92, 2.07640}, {93, 2.07780}, {94, 2.07918}, {95, 2.08055}, {96, 2.08189}, {97, 2.08322}, {98, 2.08453}, {99, 2.08583}, {100,2.08711}}