Tính tổng: A = 1x2+2x3+3x4+.......+199x200
Tính A = 1x2 + 2x3 + 3x4 + ... + 199x200
SAi rồi ! phải là 2666600 Mới đúng
Muốn biết thì bấm vào Đúng 0
Tính nhanh dãy số sau:
1x2+2x3+3x4+4x5+.....+199x200
Đặt A = 1 x 2 + 2 x 3 + ... + 199 x 200
3A = 1 x 2 x 3 + 2 x 3 x (4-1) + .... + 199 x 200 x (201 - 198)
3A = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 +.... + 199 x 200 x 201 - 198 x 199 x 200
3A = ( 1 x 2 x 3 - 1 x 2 x 3) + ( 2 x 3 x 4 - 2 x 3 x 4) + ....... + (198 x 199 x 200 - 198 x 199 x 200) + 199 x 200 x 201
Do đó A = 67 x 200 x 199 = 2666600
Đặt A=1x2+2x3+3x4+4x5+........+199x200
Ta có:
3A=1x2x3+2x3x3+3x4x3+.......+199x200x3
3A=1x2x3+2x3x(4-1)+3x4x(5-2)+....+199x200x(201-198)
3A=1x2x3+2x3x4-1x2x3+3x4x5-2x3x4+.............+199x200x201-198x199x200
3A=199x200x201
A=39800x201:3
A=39800x67
A=2666600
Vậy 1x2+2x3+3x4+........+199x200=2666600
mấy bạn thấy chưa
Uchiha Nguyễnđã được 6 cái lik e của mình đó
tính tổng:
A: 11/1x2+11/2x3+11/3x4+.....+11/199x200
B: 3-1/10-1/40-1/88-1/154
\(A=\dfrac{11}{1.2}+\dfrac{11}{2.3}+\dfrac{11}{3.4}+...+\dfrac{11}{199.200}\)
\(A=11\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{199.200}\right)\)
\(A=11\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{199}-\dfrac{1}{200}\right)\)
\(A=11\left(1-\dfrac{1}{200}\right)\)
\(A=11.\dfrac{199}{200}=\dfrac{2189}{200}\)
\(B=3-\dfrac{1}{10}-\dfrac{1}{40}-\dfrac{1}{88}-\dfrac{1}{154}\)
\(B=3-\left(\dfrac{1}{10}+\dfrac{1}{40}+\dfrac{1}{88}+\dfrac{1}{154}\right)\)
\(B=3-\left(\dfrac{1}{2.5}+\dfrac{1}{5.8}+\dfrac{1}{8.11}+\dfrac{1}{11.14}\right)\)
\(B=3-\dfrac{1}{3}\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{14}\right)\)
\(B=3-\dfrac{1}{3}\left(\dfrac{1}{2}-\dfrac{1}{14}\right)\)
\(B=3-\dfrac{3}{7}=\dfrac{18}{7}\)
D=\(\dfrac{5}{1x2}\)+\(\dfrac{5}{2x3}\)+\(\dfrac{5}{3x4}\)+....+\(\dfrac{5}{199x200}\)
\(D=\dfrac{5}{1\cdot2}+...+\dfrac{5}{199\cdot200}\)
\(=\dfrac{5}{2}\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{199}-\dfrac{1}{200}\right)\)
\(=\dfrac{5}{2}\cdot\dfrac{199}{200}=\dfrac{199}{80}\)
Lời giải:
\(D=5\times \left(\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+...+\frac{1}{199\times 200}\right)\)
\(=5\times \left(\frac{2-1}{1\times 2}+\frac{3-2}{2\times 3}+\frac{4-3}{3\times 4}+...+\frac{200-199}{199\times 200}\right)\)
\(=5\times \left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{199}-\frac{1}{200}\right)=5\times (1-\frac{1}{200})\)
\(=5\times \frac{199}{200}=\frac{995}{200}=\frac{199}{40}\)
B= \(\dfrac{1}{1x2}\)+\(\dfrac{1}{2x3}\)+\(\dfrac{1}{3x4}\)+.....+\(\dfrac{1}{198x199}\)+\(\dfrac{1}{199x200}\)
\(B=\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+...+\dfrac{1}{199\times200}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{199}-\dfrac{1}{200}\)
\(=1-\dfrac{1}{200}=\dfrac{199}{200}\)
E=\(\dfrac{0,5}{1x2}\)+\(\dfrac{0,5}{2x3}\)+\(\dfrac{0,5}{3x4}\)+......+\(\dfrac{0,5}{198x199}\)+\(\dfrac{0,5}{199x200}\)
\(E=\dfrac{0.5}{1.2}+\dfrac{0.5}{2\cdot3}+...+\dfrac{0.5}{199\cdot200}\)
\(=\dfrac{1}{2}\left(1-\dfrac{1}{200}\right)\)
\(=\dfrac{1}{2}\cdot\dfrac{199}{200}=\dfrac{199}{400}\)
Tính tổng: A = 1x2 + 2x3 + 3x4+...+99x100
Đặt A=1.2+2.3+3.4+...+99.100
3A=1.2.3+2.3.(4-1)+3.4.(5-2)+...+99.100.(101-98)
3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100
3A=99.100.101
A=333300
Tính tổng: 1x2+2x3+3x4+...+98x99
A= 1x2+2x3+3x4+...+98x99 A x 3= 1x2 x (3-0) +2x3x (4-1)+3x4 x (5-2)+...+98x99x (100-97) = 1x2x3+2x3x4+......98x99x100- (1x2x0+ 2x3x1+....+ 98x99x97) = 98x99x100
Tính tổng: 1x2+2x3+3x4+...+98x99
A= 1x2+2x3+3x4+...+98x99
A x 3= 1x2 x (3-0) +2x3x (4-1)+3x4 x (5-2)+...+98x99x (100-97)
= 1x2x3+2x3x4+......98x99x100- (1x2x0+ 2x3x1+....+ 98x99x97)
= 98x99x100.