Question

a) \(M=\dfrac{5}{1.6}+\dfrac{5}{6.11}+\dfrac{5}{11.16}+.........+\dfrac{5}{96.101}\)

b) \(N=\dfrac{1}{1.6}+\dfrac{1}{6.11}+\dfrac{5}{11.16}+........+\dfrac{1}{51.56}\)

Answer 1

`a, M = 1/1 - 1/6 + 1/6 - 1/11 + ... + 1/96 - 1/101`

`= 100/101`

`b, 5N = 5/(1.6) + 5/(6.11) + ... + 5/(51.56)`

`= 1/1 - 1/6 + 1/6 - 1/11 + ... + 1/51 - 1/56`

`= 55/56`

`=> N = 11/56`

Answer 2

\(a,M=\dfrac{5}{1.6}+\dfrac{5}{6.11}+\dfrac{5}{11.16}+....+\dfrac{5}{96.101}\)

\(M=1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+...+\dfrac{1}{96}-\dfrac{1}{101}\)

\(M=1-\dfrac{1}{101}\)

\(M=\dfrac{101-1}{101}=\dfrac{100}{101}\)

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\(b,N=\dfrac{1}{1.6}+\dfrac{1}{6.11}+\dfrac{1}{11.16}+...+\dfrac{1}{51.56}\)

\(N=1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+...+\dfrac{1}{51}-\dfrac{1}{56}\)

\(N=1-\dfrac{1}{56}\)

\(N=\dfrac{56-1}{56}=\dfrac{55}{56}\)