Simple operation of 99 times 26

Simple operation of 99 times 26

99*26
=(100-1)*26
=100*26-1*26
=2600-26
=2574

25.3 minus 0.99

Original formula = 25.3-1 + 0.01
=24.3 + 0.01 = 24.31

1/1×2+1/1-1/2:；1/2×4=1/2×（1/2-1/4）;1/58×=1/3(×1/5-1/8)
(1) According to the above formula, if M and P are positive integers, then 1 / M (M + P) = what
(2) According to the above rule: 1 / 1 × 3 + 1 / 3 × 5 + 1 / 5 × 7 +... + 1 / 99 × 101

1) If M and P are positive integers, then 1 / M (M + P) = (1 / P) (1 / M-1 / (M + P)
2)
1/(1*3)=(1/2)(1-1/3)
1/(3*5)=(1/2)(1/3-1/5)
.
1/(99*101)=(1/2)(1/99-1/101)
Original formula = (1 / 2) (1-1 / 3 + 1 / 3-1 / 5 +. + 1 / 99-1 / 101)
=(1/2)(1-1/101)=50/101

(1+1/2+1/3+.+1/60)+(2/3+2/4+2/5+.+2/60)+.+(58/59+58/60)+59/60
We must solve it

Original formula = (1) + (1 / 2) + (1 / 3 + 2 / 3) + (1 / 4 + 2 / 4 + 3 / 4) +.. + (1 / 60 + 2 / 60 +.. + 59 / 60)
Where the sum of the k-th bracket AK = (1 + 2 +.. + (k-1)) / k = (k-1) K / (2k) = (k-1) / 2
So the original formula = 1 + 1 / 2 + 2 / 2 + 3 / 2 +.. + 59 / 2 = 1 + (1 + 2 +.. + 59) / 2 = 1 + 59 * 60 / 4 = 886