có 2 tia

N=7/2(2/1.3+....+2/13.15)

N=7/2.(1/1-1/3+.....+1/13-1/15)

N=7/2.(1-1/15)

N=7/2.(14/15)

N=7.14/2.15

Bạn giải M luôn dc ko?

C = 1² + 2² +3² + 4² + ......+ 2018²

C= 1.1 + 2.2 + 3.3 + .....+ 2018.2018

C= 1 + 2 . ( 1+1) + 3 . (2+1)+.......+ 2018 . (2017+1)

C= 1+ 1.2 + 2 + 2.3 + 3 + ........+ 2017.2018 + 2018

C= ( 1.2 + 2.3 + 3.4 + ....+ 2017.2018 ) + ( 1+2+3+...+2018)

đặt A = 1.2 + 2.3 + 3.4 +...+ 2017.2018

     3A = 1.2.(3-0) + 2.3. (4-1) + ......+ 2017.2018.(2019-2016)

    3A = (1.2.3 + 2.3.4 +.....+ 2017.2018.2019) - ( 1.2.3 + 2.3.4 + .....+ 2016.2017.2018)

    3A = 2017.2018.2019=> A= (2017. 2018 . 2019) : 3 = 2739315938(1)

đặt B= 1+2+3+...+2018

     B=  [(2018 + 1) . 2018 ] : 2 = 2037171(2)

thay (1) (2) vào C ta có C = 2739315938 + 2037171= 2741353109

vậy ...... chúc hok tốt

nếu a=b => a/b=1

=> nếu a>b thì a/b>1

đặt A=1/2×3+1/2×3×4+1/3×4×5+...+1/48×49×50

2A=2.(1/2×3+1/2×3×4+1/3×4×5+...+1/48×49×50)

2A=2/1.2.3+2/2.3.4+......+2/48.49.50

2A=1/2-1/2.3+1/2.3-1/3.4+.....+1/48.49-1/49.50

2A=1/2-1/49.50

A=1/2-1/49.50):2

Ta có: \(\frac{31}{2}.\frac{32}{2}...\frac{60}{2}=\frac{31.32...60}{2^{30}}=31.33...57.59.\left(\frac{32.34...58.60}{2^{30}}\right)\)

                                                                         \(=31.33...57.59.\left(\frac{16.17...29.30}{2^{15}}\right)=17.19...27.29.31.33...57.59.\left(\frac{16.18...30}{2^{15}}\right)\)

\(=17.19...57.59.\left(\frac{8.9...15}{2^7}\right)=9.11.13.15.17...57.59.\left(\frac{8.10.12.14}{2^7}\right)\)

\(=9.11...57.59.\left(\frac{4.5.6.7}{2^3}\right)=5.7.9...57.59.\left(\frac{4.6}{2^3}\right)\)

\(=5.7.9...57.59.3=1.3.5...59\)

   57 . 49 + 37 . 50 + 37

= 37 ( 50 + 1 ) + 57 . 49 

= 37 . 51 + 57 . 49 ( đến chỗ này thì không thể tính nhanh đc sr )

= 1887 + 2793

= 4680

Mình ngĩ nếu đề bài thế này còn tính nhanh đc nà : 57 . 49 + 37 . 50 - 37 ( nghĩ zậy thui :3 )

\(D=\frac{1}{100.99}-\frac{1}{99.98}-\frac{1}{98.97}-...-\frac{1}{3.2}-\frac{1}{2.1}\)

\(D=\frac{1}{99.100}-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{97.98}+\frac{1}{98.99}\right)\)

\(D=\frac{1}{99}-\frac{1}{100}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{98}-\frac{1}{99}\right)\)

\(D=\frac{1}{99}-\frac{1}{100}-\left(1-\frac{1}{99}\right)\)

\(D=\frac{1}{99}-\frac{1}{100}-1+\frac{1}{99}\)

b tự làm nốt nhé

D=1100.99 −199.98 −198.97 −...−13.2 −12.1 

D=199.100 −(11.2 +12.3 +...+197.98 +198.99 )

D=199 −1100 −(1−12 +12 −13 +...+198 −199 )

D=199 −1100 −(1−199 )

D=199 −1100 −1+199