Question

tính tổng S=1+1/2+1/2^2+1/2^4+1/2^6+...+1/2^98+1/2^100

Answer 1

Sửa đề: \(S=1+\frac{1}{2^2}+\frac{1}{2^4}+\cdots+\frac{1}{2^{98}}+\frac{1}{2^{100}}\)

Ta có: \(S=1+\frac{1}{2^2}+\frac{1}{2^4}+\cdots+\frac{1}{2^{98}}+\frac{1}{2^{100}}\)

=>\(4S=4+1+\frac{1}{2^2}+\cdots+\frac{1}{2^{96}}+\frac{1}{2^{98}}\)

=>\(4S-S=4+1+\frac{1}{2^2}+\cdots+\frac{1}{2^{98}}-1-\frac{1}{2^2}-\cdots-\frac{1}{2^{100}}\)

=>\(3S=4-\frac{1}{2^{100}}=\frac{2^{102}-1}{2^{100}}\)

=>\(S=\frac{2^{102}-1}{3\cdot2^{100}}\)

Answer 2

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