1/1.2+1/3.4+1/5.6+...+1/49.50=1/26+1/27+...+1/50

Question

hiennhi · Answer

`1/1.2 + 1/3.4 + 1/5.6 +...+ 1/49.50`   `= 1 -1/2 + 1/3 -1/4 + 1/5- 1/6 +...+ 1/49 -1/50`   `= (1 + 1/3 + 1/5 +...+ 1/49) - ( 1/2 + 1/4 + 1/6+...+1/50)`   `= (1+ 1/2 + 1/3 + 1/4+...+ 1/49 + 1/50) - 2(1/2 + 1/4 +...+1/50)`   `=1 + 1/2 + 1/3 + 1/4 +...+1/50 - 1 - 1/2 - ...- 1/25`   `=1/26 + 1/27 + 1/28 +...+ 1/50`

cattuong · Answer

1/1.2+1/3.4+....+1/49.50=(2-1)/1.2+(4-3)/3.4+....+(50-49)/50.49=1-1/2+1/3-....-1/50=(1+1/3+1/5+....+1/49)-(1/2+1/4+...+1/50)=(1+1/2+1/3+....+1/50)-2(1/2+1/4+....+1/50)=(1+1/2+....+1/50)-(1+1/2+1/3+....+1/25)=1/26+1/27+....+1/50

1/1.2+1/3.4+1/5.6+…+1/49.50=1/26+1/27+…+1/50

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