Question

[Thảo Fami]

Chứng minh rằng : 

a,1- 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + ...... + 1/ 99 - 1/ 100 = 1 / 51 + 1/ 52 + 1/ 53 + ... + 1/ 100

b, A= 1/3 - 2/ 3² + 3/ 3³ - 4/ 3⁴ + .... + 99/ 3⁹⁹ - 100/ 3¹⁰⁰ < 3/ 16

Answer 1

[✓ ℍɠŞ_ŦƦùM $₦G ✓]

\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}=\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{99}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{100}\right)\)

\(=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{99}+\frac{1}{100}\right)-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{100}\right)\)

\(=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{50}\right)=\frac{1}{51}+\frac{1}{52}+...+\frac{1}{100}\)

\(\RightarrowĐPCM\)

Answer 2

[Nguyễn Khắc Kiệt]

giúp tui phần b bài này