Câu 2.4: Tính nhanh:
\(A = {1 \over 3} – {3 \over 4} – \left( { – {3 \over 5}} \right) + {1 \over {72}} – {2 \over 9} – {1 \over {36}} + {1 \over {15}}\).
\(A = \left( {{1 \over 3} + {3 \over 5} + {1 \over {15}}} \right) – \left( {{3 \over 4} + {2 \over 9} + {1 \over {36}}} \right) + {1 \over {72}} \)
\(= 1 – 1 + {1 \over {72}} = {1 \over {72}}\)
Câu 2.5: Tính nhanh:
\(B = {1 \over 5} – {3 \over 7} + {5 \over 9} – {2 \over {11}} + {7 \over {13}} – {9 \over {16}} – {7 \over {13}} +\)
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\({2 \over {11}} – {5 \over 9} + {3 \over 7} – {1 \over 5}\)
\(B = \left( {{1 \over 5} – {1 \over 5}} \right) + \left( { – {3 \over 7} + {3 \over 7}} \right) + \left( {{5 \over 9} – {5 \over 9}} \right) +\)
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\(\left( { – {2 \over {11}} + {2 \over {11}}} \right) + \left( {{7 \over {13}} – {7 \over {13}}} \right) – {9 \over {16}}\)
\( \Leftrightarrow B = 0 + 0 + 0 + 0 + 0 – {9 \over {16}}\)
\(\Leftrightarrow B = – {9 \over {16}}\)
Câu 2.6: Tính nhanh:
\(C = {1 \over {100}} – {1 \over {100.99}} – {1 \over {99.98}} – {1 \over {98.97}} – … – {1 \over {3.2}} – {1 \over {2.1}}\)
\(C = {1 \over {100}} – \left( {{1 \over {1.2}} + {1 \over {2.3}} + … + {1 \over {98.99}} + {1 \over {99.100}}} \right)\)
= \({1 \over {100}} – \left( {1 – {1 \over 2} + {1 \over 2} – {1 \over 3} + … + {1 \over {98}} – {1 \over {99}} + {1 \over {99}} – {1 \over {100}}} \right)\)
= \({1 \over {100}} – \left( {1 – {1 \over {100}}} \right) = {1 \over {100}} – {{99} \over {100}} = {{ – 98} \over {100}} = – {{49} \over {50}}\)
