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Calculation:1+2+2 squared +2 cube +2 to the 100th power
1+2+2 Square +2 cube +2 100th power
Let s=1+2+2 squared+2 cubic+2 to the 100th power
2S=2+2^2+2^3+.2^100+2^201
S=2s-s=2^201-1
Given S=12-22+32-42+...+992-1002+1012, the remainder of S divided by 103 is ______.
Original formula=12+(3+2)(3-2)+(5+4)(5-4)+...+(101+100)(101-100)
=1+5+9+…+201
=51(1+201)
2
=5151.
Because 5151
103=50…1,
So the remainder of S divided by 103 is 1.
Therefore, the answer is:1.
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