1/1X2X3+1/2X3x4+…+1/48X49X50

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1/1X2X3+1/2X3x4+…+1/48X49X50
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1/1X2X3+1/2X3x4+…+1/48X49X50
1/1X2X3+1/2X3x4+…+1/48X49X50

1/1X2X3+1/2X3x4+…+1/48X49X50
1/1X2X3+1/2X3x4+…+1/48X49X50
=(1/1X2-1/2X3+1/2X3-1/3x4+…+1/48X49-1/49X50)÷2
= (1/1X2-1/49X50)÷2
=(1/2-1/2450)÷2
=1224/2450÷2
=306/1225

=1/2x(1/1x2-1/2x3)+1/2x(1/2x3-1/3x4)+……+1/2x(1/48x49-1/49x50)
=1/2x(1/1x2-1/2x3+1/2x3-1/3x4+……+1/48x49-1/49x50)
=1/2x(1/1x2-1/49x50)
=306/1225