Question

\(B=\frac{2}{1x2}+\frac{2}{2x3}+...+\frac{2}{100x101}\)

Answer 1

\(\frac{B}{2}=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{100\cdot101}\)

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

\(\frac{B}{2}=\frac{100}{101}\)

\(B=\frac{200}{101}\)

Answer 2

B = \(2\left(\frac{1}{1x2}+\frac{1}{2x3}+....+\frac{1}{100x101}\right)\)

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

B = \(2\left(1-\frac{1}{101}\right)\)

B = \(2x\frac{100}{101}\)

B = \(\frac{200}{101}\)

Answer 3

\(B=\frac{2}{1\cdot2}+\frac{2}{2\cdot3}+\frac{2}{3\cdot4}+...+\frac{2}{100\cdot101}\)

\(B=2\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{100\cdot101}\right)\)

\(B=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{100}-\frac{1}{101}\right)\)

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

\(B=2\cdot\frac{100}{101}\)

\(B=\frac{200}{101}\)

Answer 4

Answer 5

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Answer 6

B = 2/1×2 + 2/2×3 + .... 2/100×101 

B = 2 × ( 1/1×2 + 1/2×3 +... + 1/100×101 ) 

B = 2 × ( 1 - 1/2 + 1/2 - 1/3 + .... + 1/100 - 1/101 )

B = 2 × ( 1 - 1/101 )

B = 2 × ( 101/101 - 1/101 ) 

B = 2 × 100/101

B =  200/101