Question

[PHẠM LÊ THÁI AN]

a) 1/2×3+1/3×4+1/4×5+...+1/x×(x+1)=49/100 b) x-20/11×13-20/13×15-...-20/53/55=3/11

Answer 1

[Xyz OLM]

\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}=\frac{49}{100}\)

<=> \(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{49}{100}\)

<=> \(\frac{1}{2}-\frac{1}{x+1}=\frac{49}{100}\)

<=> \(\frac{1}{x+1}=\frac{1}{100}\)

<=> x + 1 = 100

<=> x = 99

b) \(x-\frac{20}{11.13}-\frac{20}{13.15}-...-\frac{20}{53.55}=\frac{3}{11}\)

<=> \(x-10.\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{53.55}\right)=\frac{3}{11}\)

<=> \(x-10.\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{11}\)

<=> \(x-10.\left(\frac{1}{11}-\frac{1}{55}\right)=\frac{3}{11}\)

<=> \(x-\frac{8}{11}=\frac{3}{11}\)

<=> x = 1

Vậy x = 1

P/S : Dấu "." là dấu "x" 

Answer 2

[PHẠM LÊ THÁI AN]

Thank you nha