Question

A= \(\dfrac{101+100+99+98+...+3+2+1}{101-100+99-98+...+3+2+1}\)

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Answer 1

A= \(\dfrac{\left(101+1\right)+\left(100+2\right)+...+\left(99+3\right)}{\left(101+1\right)-\left(100+2\right)+...+\left(99+3\right)-\left(98+3\right)}\)

= \(\dfrac{50.101}{50}\)

= 101

Answer 2

\(A=\dfrac{101+100+99+98+...+3+2+1}{101-100+99-98+...+3-2+1}\)

\(A=\dfrac{\left[\left(101-1\right):1+1\right].\left(101+1\right):2}{1.50+1}\)

\(A=\dfrac{5151}{51}=101\)