1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8...1/49*50

1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8...1/49*50

1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8...1/49*50=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+…… +(1/49-1/50)=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+…… +1/49...

2*1+4*3+6*5+8*7+10*9+.+50*49
Hurry, come and help me

2*1+4*3+6*5+8*7+10*9+.+50*49=(2^2+4^2+6^2+.+50^2)-(2+4+6+…… +50) = 4 * (1 + 2 ^ 2 + 3 ^ 2 + 4 ^ 2 +. + 25 ^ 2) - (2 + 50) * 25 / 2 = 4 * 25 (25 + 1) (2 * 25 + 1) / 6-650 = 132600 / 6-650 = 25450. This is what happened in the process. I didn't calculate the final number carefully

1/1×3+1/3×5+1/5×7+………… +1 / 49 × 51 and 1 / 2 × 4 + 1 / 4 × 6 + 1 / 6 × 8 + 1/48×50
Then there is 1 / 1 + 2 + 1 / 1 + 2 + 3 + + 1/1+2+3+…… +100
I'll use it for class tomorrow

1/1×3+1/3×5+1/5×7+………… +1/49×51=（1-1/3+1/3-1/5+1/5-1/7+…… +1/49-1/51）÷2=（1-1/51）÷2=50/51÷2=25/511/2×4＋1/4×6＋1/6×8＋………… 1/48×50=（1/2-1/4+1/4-1/6+1/6-1/8+…… +1/49-1/50）÷2=（...