Question

chứng tỏ tổng sau nhỏ hơn 2:B=10/1x6+10/6x11+10/11x16+.....+10/46x51

câu này khó quá hà,trả lời giùm nha!thank you nhìu lắm

Answer 1

Ta có:

B = 10/1.6 + 10/6.11 + 10/11.16 + ... + 10/46.51

B = 2(5/1.6 + 5/6.11 + 5/11.16 + ... + 5/46.51)

B = 2 . (1 - 1/6 + 1/6 - 1/11 + 1/11 - 1/16 + ... + 1/46 - 1/51)

B = 2. (1 - 1/51)

B = 2.50/51

B = 100/51 < 102/51 = 2

=> Ta có đpcm

Answer 2

\(B=\dfrac{10}{1.6}+\dfrac{10}{6.11}+\dfrac{10}{11.16}+.....+\dfrac{10}{46.51}\)

\(B=2\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+.....+\dfrac{1}{46}-\dfrac{1}{51}\right)\)

\(B=2\left(1-\dfrac{1}{51}\right)\)

\(B=2-\dfrac{2}{51}\)

\(B< 2\left(đpcm\right)\)