51×52+52×53+53×54+...+100×101=

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51×52+52×53+53×54+...+100×101=
51×52+52×53+53×54+...+100×101=

51×52+52×53+53×54+...+100×101=
n(n+1)=n^2+n
1^2+2^2+……+n^2
=n(n+1)(2n+1)/6
1^2+2^2+……+100^2
=100*101*201/6
=338350
1^2+2^2+……+50^2
=50*51*101/6
=42925
51^2+52^2+……+100^2
=338350-42925
=295425
51×52+52×53+53×54+...+100×101
=51^2+51+52^2+52+……+100^2+100
=51^2+52^2+……+100^2+51+52+……+100
=295425+(51+100)*100/2
=295425+7550
=302975