LetSk, k=1,2, …,100, denote the sum of the infinite geometric series whose first term iskk!and the common ratio is1k.Then, the value of1002100!+100∑k=2|(k2k+1)Sk|is :1243LetSk, k=1,2, …,100, denote the sum of the infinite geometric series whose first term iskk!and the common ratio is1k.Then, the value of1002100!+100∑k=2|(k2k+1)Sk|is :1243Sk, k=1,2, …,100Sk, k=1,2, …,100Sk, k=1,2, …,100SkSSSkkkkk,, kk==11,,22,, ……,,100100kk!kk!kk!kk!kk!kk!kk!kkkk−1k!k!kk!!1k1k1k1k1k1k1k111kkk1002100!+100∑k=2|(k2k+1)Sk|1002100!+100∑k=2|(k2k+1)Sk|1002100!+100∑k=2|(k2k+1)Sk|1002100!+100∑k=2|(k2k+1)Sk|1002100!+100∑k=2|(k2k+1)Sk|1002100!1002100!1002100210010010022222100!100!100100!!++100∑k=2100∑k=2100∑100∑100∑100100100100100∑∑∑k=2k=2k=2k=2kk==22||||((k2kkk22222−kk++11))SkSSSkkkkk||||111111222222444444333333A1111111B4444444C3333333D2222222?