Bài 25:
A = 2^100 - 2^99 - 2^98 -...- 2^2 - 2 - 1
2A = 2 . ( 2^100 - 2^99 - 2^98 - ... - 2^2 -2-1)
2A = 2^101 - 2^100 - 2^99 - ... - 2^2 - 2
2A - A = 2^101 - 2^100 - 2^100 +1
A = 2^101 -2 . 2^100 + 1
A = 2^101 - 2^101 + 1
A = 1
B = 1/1.2.3 + 1/2.3.4 + 1/3.4.5 +...+1/37.38.39
B = 1/1.2 - 1/2.3 + 1/2.3 - 1/3.4 +....+ 1/37.38 - 1/38.39
B = 1/1.2 - 1/38/39
B = 370/714
C = 1.2 + 2.3 +...+ 99.100
3C = 1.2.3 + 2.3.3 + ... + 99.100.3
3C = 1.2 . (3-0) + 2.3 . (4-1) +...+ 99.100 . (101-98)
C = 99 . 100 . 101/3
C = 333300
D = (1-1/3) . (1-1/6) . (1-1/10) . (1-1/15) ... (1-1/780)
D = 2/3 . 5/6 . 9/10 ...... . 779/780
D = 4/6 . 10/12 . 18/20 ......1558/1560
D = 1.4/2.3 . 2.5/3.4 . 3.6/4.5 ...... 38.4/39.40
D = 1.2.3....38 / 2.3.4....39 . 4.5....41/ 3.4.....40
D = 1/39 . 41/3
D = 41/117
E =5/2.1 + 4/1.11 + 3/11.2 + 1/2.15 + 13/15.4
E/7 = 5/2.7 + 4/11.7 + 3/11.14 + 1/14.15 + 13/15.4
E/7 =1/2 - 1/7 + 1/7 - ... + 1/15 1/28
E/7 = 1/2 - 1/28
E/7 = 13/28
E = 13/28 . 7
E = 13/4
Bạn ơi, xl nha, mik ko bt làm bài chứng minh!