+288 Calculate
11⋅2⋅3+12⋅3⋅4+...+199⋅100⋅101
(A)502920200 (B)503920200 (C)304920200 (D)50920200 (E)504920200
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+26396 Calculate
11⋅2⋅3+12⋅3⋅4+…+199⋅100⋅101
11⋅2⋅3+12⋅3⋅4+…+199⋅100⋅101=99∑n=11n(n+1)(n+2)=99∑n=11n(1(n+1)(n+2))=99∑n=11n(1n+1−1n+2)=99∑n=1(1n(n+1)−1n(n+2))=99∑n=1(1n−1n+1−12(1n−1n+2))=99∑n=1(12n−1n+1+12(n+2))=99∑n=112n−99∑n=11n+1+99∑n=112(n+2)
99∑n=112n−99∑n=11n+1+99∑n=112(n+2)=1299∑n=11n−99∑n=11n+1+1299∑n=11n+2=1297∑n=−11n+2−98∑n=01n+2+(12∗1100+12∗1101+1297∑n=11n+2)=(12∗11+12∗12+1297∑n=11n+2)−98∑n=01n+2+(12∗100+12∗101+1297∑n=11n+2)=(12+14+1297∑n=11n+2)−12−98∑n=11n+2+(12∗100+12∗101+1297∑n=11n+2)=(12+14+1297∑n=11n+2)−12−1100−97∑n=11n+2+(12∗100+12∗101+1297∑n=11n+2)=12+14−12−1100+1200+1202+1297∑n=11n+2−97∑n=11n+2+1297∑n=11n+2=14−1100+1200+1202+97∑n=11n+2−97∑n=11n+2=14−1100+1200+1202=14−2200+1200+1202=14−1200+1202=12(12−1100+1101)=12(98200+1101)=12(98∗101+200200∗101)=49∗101+100200∗101=504920200
