tính nhanh (2/3+3/4+5/6+...+99/100).(1/2+2/3+3/4+...+98/99)-(1/2+1/3+...+99/100).(2/3+2/4+...+98/99)

Rút gọn

A= 2^100+2^99+2^98.....+2+1

B=3^100+3^99+3^98....+3+1

C=4^100+4^99+....+4+1

D=2^100- 2^99+....+2^2 - 2 + 1

E=3^100 - 3^99 + 3^98....- 3 +1

Thu gọn

M= 2 + 2^2 + 2^3 ....+ 2^100

Cho A =2+2^2+2^3+....2^100. Tìm số tự nhiên x sao cho A + 1 = 2x

1/1*2   1/2*3  1/3*4  .....  -1/98*99=1/100 1/99*100

S=1×2+2×3+3×4+4×5+...........+99×100

3S=1×2×3+2×3×(4-1)+3×4×(5-2)+4×5×(6-3)+............+99×100×(101-98)

3S=1×2×3+2×3×4-1×2×3+3×4×5-2×3×4+4×5×6-3×4×5+.............+99×100×101-98×99×100

3S=99×100×101

Tại sao 3S=99×100×101

Các bạn giải thích hộ mình với!

MÌNH CẢM ƠN MỌI NGƯỜI!

B=3^100-3^99-3^98-..-3-1

B=3^100-(3^99+3^98+...+3+1)

ta có:M=3^99+3^98+..+3+1

3M=3^100+3^98+...+3^2+3

2M=3M-M=3^100+3^99+3^98+...+3^2+3-3^99+3^98+...+1

2M=3^100-1

=>B=3^100-3^100+1:2

B=0+1/2

B=1/2

1)11-12+13-14+15-16+17-18+19-20+21-22+.........+99-100

2)2-4+6-8+......+1998-2000

3)-1+3-5+7-....+97-99

4)1+2-3-4+.........+97+98-99-100

5)1-2+3-4+.............+99-100

6)1+3-5-7+......+97-98-99+100

7)2¹⁰⁰-2⁹⁹-2⁹⁸-..........2²-2-1

8)1-4+7-10+........+307-310+313

bài 1

A=1*2*3+2*3*4+3*4*5+...+99*100*101

B=1*3*5+3*5*7+...+95*97*99

C=2*4+4*6+..+98*100

D=1*2+3*4+5*6+...+99*100

E=1^2+2^2+3^2+...+100^2

G=1*3+2*4+3*5+4*6+...+99*101+100*102

H=1*2^2+2*3^2+3*4^2+...+99*100^2

I=1*2*3+3*4*5+5*6*7+7*8*9+...+98*99*100

K=1^2+3^2+5^2+...+99^2

1/1*2*3+1/2*3*4+1/3*4*5+........+1/98*99*100=1/k*(1/1*2-1/99*100)

A = 1 . 2 + 2 . 3 + 3 . 4 + ......... + 98 . 99 / 1 + ( 1 + 2 ) + ( 1 + 2 + 3 ) + ........... + ( 1 + 2 + 3 + ...... + 98 )

B = ( 1 / 51 . 52 ) + 1 / 52 . 53 + ...... + 1 / 100 . 101 ) : ( 1 / 1 . 2 + 1 / 2 . 3 + ........ + 1 / 99 . 100 + 1 / 100 . 101