An algebra problem by أحمد الحلاق

Algebra Level 4

Consider the 50-term sums:
S = 1 1 ⋅ 2 + 1 3 ⋅ 4 + ⋯ + 1 99 ⋅ 100 S = \dfrac1{1\cdot 2 } +\dfrac1{3\cdot4} + \cdots + \dfrac1{99\cdot100} .
T = 1 51 ⋅ 100 + 1 52 ⋅ 99 + ⋯ + 1 99 ⋅ 52 + 1 100 ⋅ 51 T = \dfrac1{51\cdot 100 } + \dfrac1{52\cdot99} + \cdots + \dfrac1{99\cdot 52} + \dfrac1{100\cdot 51} .

Find S T \dfrac ST .


The answer is 75.5.

أحمد الحلاق by أحمد الحلاق , 28, Palestine

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