Question

1/2 + 1/4 + 1/8 + 1/16 + ............ + 1/152

Answer 1

Đặt tổng trên = A

\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{16}+...+\frac{1}{152}\)

\(Ax2=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{16}+...+\frac{1}{76}\)

\(Ax2-A=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{16}+...+\frac{1}{76}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{16}+...+\frac{1}{152}\right)\)

\(A=1-\frac{1}{152}\)

\(A=\frac{151}{152}\)

Answer 2

\(\text{Đặt tổng trên = A}\)

\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{16}+...+\frac{1}{152}\)

\(Ax2=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{16}+...+\frac{1}{76}\)

\(Ax2-A=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{16}+...+\frac{1}{76}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{16}+...+\frac{1}{152}\right)\)

\(A=1-\frac{1}{152}\)

$A=\frac{151}{152}$