Đáp án:
A = 250000
B = 49600
C = 1275
F = 51
Giải thích các bước giải:
A = 1 + 3 + 5 + 7 + ... + 999
A = (1+999) + (3+997) + (5+995) + (7+993) + ...
A = $\underbrace{1000 + 1000 + 1000 + 1000 + ...}_{[(999-1):2+1]:2=250}$
A = 1000 * 250
A = 250000
B = 1 + 11 + 21 + 31 + ... + 991
B = (1+991) + (11+981) + (21+971) + (31+961) + ...
B = $\underbrace{992+992+992+992+...}_{[(991-1):10+1]:2=50}$
B = 992 * 50
B = 49600
C = 3 + 7 + 11 + 15 + ... + 99
C = (3+99) + (7+95) + (11+91) + (15+87) + ...
C = $\underbrace{102+102+102+102+...}_{[(99-3):4+1]:2=25:2}$
C = 102 * 25 : 2
C = 1275
F = 1 - 2 + 3 - 4 + 5 - 6 + ... + 99 - 100 + 101
F = (1 + 3 + 5 + 7 + ... + 101) - (2 + 4 + 6 + 8 + ... + 100)
F = [(1+101) + (3+99) + (5+97) + (7+95) + ...] - [(2+100) + (4+98) + (6+96) + (8+94) + ...]
F = $\underbrace{102+102+102+102+...}_{[(101-1):2+1]:2=51:2}$ - $\underbrace{102+102+102+102+...}_{[(100-2):2+1]:2=25}$
F = 102 * 51 : 2 - 102 * 25
F = 51
