Question

CMR: 1/2² +1/2³+1/2⁴+...+1/2⁸<1

Answer 1

\(A=\left(\dfrac{1}{2}\right)^2+\left(\dfrac{1}{2}\right)^3+...+\left(\dfrac{1}{2}\right)^8\)

=>\(2A=\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2+...+\left(\dfrac{1}{2}\right)^7\)

=>\(A=\dfrac{1}{2}-\left(\dfrac{1}{2}\right)^8=\dfrac{1}{2}-\dfrac{1}{2^8}=\dfrac{2^7-1}{2^8}\)<1

Answer 2

So sánh M=1/1.2+1/2.3+...+1/49.50 với 1