Giải sum_k=1^991/(k+1)sqrt{k+k+sqrt{k}+1}

$$\sum _ { k = 1 } ^ { 99 } \frac { 1 } { ( k + 1 ) \sqrt { k } + k + \sqrt { k } + 1 }$$

Tính giá trị

$$\frac{28\sqrt{26}}{19655}+\frac{31\sqrt{29}}{26969}+\frac{32\sqrt{30}}{29759}+\frac{33\sqrt{31}}{32735}+\frac{35\sqrt{33}}{39269}+\frac{36\sqrt{34}}{42839}+\frac{37\sqrt{35}}{46619}+\frac{39\sqrt{37}}{54833}+\frac{40\sqrt{38}}{59279}+\frac{41\sqrt{39}}{63959}+\frac{43\sqrt{41}}{74045}+\frac{44\sqrt{42}}{79463}+\frac{45\sqrt{43}}{85139}+\frac{48\sqrt{46}}{103775}+\frac{49\sqrt{47}}{110543}+\frac{53\sqrt{51}}{140555}+\frac{55\sqrt{53}}{157409}+\frac{57\sqrt{55}}{175559}+\frac{59\sqrt{57}}{195053}+\frac{60\sqrt{58}}{205319}+\frac{61\sqrt{59}}{215939}+\frac{63\sqrt{61}}{238265}+\frac{64\sqrt{62}}{249983}+\frac{67\sqrt{65}}{287429}+\frac{68\sqrt{66}}{300695}+\frac{69\sqrt{67}}{314363}+\frac{71\sqrt{69}}{342929}+\frac{72\sqrt{70}}{357839}+\frac{73\sqrt{71}}{373175}+\frac{75\sqrt{73}}{405149}+\frac{76\sqrt{74}}{421799}+\frac{79\sqrt{77}}{474473}+\frac{80\sqrt{78}}{492959}+\frac{81\sqrt{79}}{511919}+\frac{84\sqrt{82}}{571703}+\frac{85\sqrt{83}}{592619}+\frac{87\sqrt{85}}{635969}+\frac{88\sqrt{86}}{658415}+\frac{89\sqrt{87}}{681383}+\frac{91\sqrt{89}}{728909}+\frac{93\sqrt{91}}{778595}+\frac{95\sqrt{93}}{830489}+\frac{96\sqrt{94}}{857279}+\frac{97\sqrt{95}}{884639}+\frac{99\sqrt{97}}{941093}+\frac{2527077\sqrt{13}}{406137967}+\frac{3351804\sqrt{14}}{621868465}+\frac{4363419\sqrt{15}}{925602601}+\frac{7054161\sqrt{17}}{1909215907}+\frac{10830279\sqrt{19}}{3642054445}+\frac{15950397\sqrt{21}}{6524164375}+\frac{19102836\sqrt{22}}{8559345697}+\frac{22700787\sqrt{23}}{11098025137}+\frac{67754637984\sqrt{7}}{3211143127583}+\frac{731344006452\sqrt{10}}{68454622774079}+\frac{1389000224448\sqrt{11}}{156184708751015}+\frac{4024974600893480\sqrt{5}}{99821256811279201}+\frac{4545318199417604\sqrt{6}}{158628783237794525}+\frac{257187424997806755\sqrt{3}}{2470142111309259409}+\frac{275249017898278339874810456\sqrt{2}}{1261947316203966525147607327}-\frac{5920290908712302332513543524256538141346667407366639211772006780209806217941714883675338900814522118261428952385264285818258410381776779369903275562726520361279656158451378536390950769523750596367481456663305120937321605623474566312709653190733207603861547793572564750292590925728010198397072435576022551070546337663008130916059663561886634969416131978002846044947620346988}{126879079545852973587577842880210973530967709410175702657373582793946035512165493227170017882899607003490483975910527040417442331242933366838175873369226550882964907020430852956330885873798624087668566153564426176843922424661028104617012019875771532766627311145560350533900962365360860862155058668106847541271600436380026281382813175314337995534117146906695620632506451526875}$$