Question

S=2/1.2+2/2.3+2/3.4+2/4.5+.........2/101.102

Answer 1

Trä Loi Bhangra nhé

Answer 2

S = 2/1×2 + 2/2×3 + 2/3×4 + 2/4×5 + ... + 2/101×102

B = 2 × (1/1×2 + 1/2×3 + 1/3×4 + 1/4×5 + ... + 1/101×102)

B = 2 × (1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/101 - 1/102)

B = 2 × (1 - 1/102)

B = 2 × 101/102

B = 101/51

Answer 3

\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+....+\frac{2}{100.101}\)

\(=2.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{100.101}\right)\)

\(=2.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{100}-\frac{1}{101}\right)\)

\(=2.\left(1-\frac{1}{101}\right)\)

\(=2.\frac{100}{101}=\frac{200}{101}\)