gọi biểu thức trên là A, ta có
\(A=\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{152}\)
→\(2A=2\left(\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{152}\right)\)
\(2A=1+\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{76}\)
→\(2A-A=\left(1+\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{76}\right)-\left(\dfrac{1}{2}+\dfrac{1}{4}+..+\dfrac{1}{152}\right)\)
→\(A=1-\dfrac{1}{152}\)
→\(A=\dfrac{151}{152}\)
VẬY 1/2+1/4+1/8+...+1/152 =151/152
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