Question

                                                     Các bạn giỏi toán ơi làm giúp mình 2 câu này với nha!!!!!
1. Tính:
\(C=\frac{2^2}{3}.\frac{3^2}{8}.\frac{4^2}{15}.\frac{5^2}{24}.\frac{6^2}{35}.\frac{7^2}{48}.\frac{8^2}{63}.\frac{9^2}{80}\)
\(D=\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+\frac{5}{7.9}+.....+\frac{5}{97.99}\)


                                                                          CẢM ƠN CÁC BẠN NHIỀU!!!!!
 

Answer 1

C=\(\frac{2.2}{1.3}\).\(\frac{3.3}{2.4}\).....\(\frac{9.9}{8.10}\)=\(\frac{2.2.3.3...9.9}{1.3.2.4...8.10}\)= \(\frac{2.9}{1.10}\)= \(\frac{9}{5}\)

Answer 2

\(D.=\frac{5}{2}.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{97}-\frac{1}{99}\right)\)

\(D=\frac{5}{2}.\left(\frac{1}{1}-\frac{1}{99}\right)\)

\(D=\frac{5}{2}.\frac{98}{99}\)

\(D=\frac{245}{99}\)

Answer 3

\(C=\frac{2^2.3^2.4^2.5^2.6^2.7^2.8^2.9^2}{3.8.15.24.35.48.63.80}\)

\(C=\frac{2.2.3.3.4.4.5.5.6.6.7.7.8.8.9.9}{3.2.4.3.5.4.6.5.7.6.8.7.9.8.10}\)

Giản ước đi :

 \(C=\frac{2.3.4.5.6.7.8.9}{10}\)

\(C=36288\)

Answer 4

C=2²/3 . 3²/8 .4²/15 .5²/24 .6²/35 .7²/48 .8²/63 .9²/80

  =(2.2.3.3.4.4.5.5.6.6.7.7.8.8.9.9)/(3.2.4.3.5.4.6.5.7.6.8.7.9.8.10)

  = 2/10=1/5

D=5/1.3+5/3.5+5/5.7+5/7.9+...+5/97.99

  = 5/2(2/1.3+2/3.5+2/5.7+2/7.9+...+2/97.99)

  =5/2(1/1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+...+1/97-1/99)

  =5/2(1-1/99)

  =5/2.98/99=245/99

Answer 5

C=(2x2x3x3x4x4x5x5x6x6x7x7x8x8x9x9) : (1x3x2x4x3x5x4x6x5x7x6x8x7x9x8x10)

C=(2x2x3x3x4x4x5x5x6x6x7x7x8x8x9x9) : (1x2x3x3x4x4x5x5x6x6x7x7x8x8x9x10)

C=18 : 10

C=9 : 5

(mình viết : thay cho phân số đấy)

D=5x(1:1x3 + 1 : 3x5 +..........+1 : 97 x 99)

2D=5x(2 : 1x3 + 2 : 3x5+......+2 : 97x99)

2D=5x(1:1 - 1:3+...+1:97-1:99)

2D=5x(1:1 - 1:99)

2D=5x98:99

2D=490:99

D=490:99:2

D=245:99

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