Tinh 2S, roi lay 2S-S=1-1/2^100

ban co the giai thich cu the hon duoc khong?

=)2S-S=(1+1/2+1/2^2+......+1/2^99)-(1/2+1/2^2+1/2^3+......+1/2^100)

=)S=1-1/2^100

=)S=2^100-1/2^100

Cứ chép vào đáp ản chuẩn nhớ là ko cần tính rõ ra=)))

\(S=1+\frac{1}{3}+\frac{1}{3^2}+........+\frac{1}{3^n}\)

\(3S=3+1+\frac{1}{3}+.......+\frac{1}{3^{n-1}}\)

\(\Rightarrow3S-S=\left(3+1+\frac{1}{3}+......+\frac{1}{3^{n-1}}\right)-\left(1+\frac{1}{3}+\frac{1}{3^2}+......+\frac{1}{3^n}\right)\)

\(\Rightarrow2S=3-\frac{1}{3^n}\Rightarrow2S=\frac{3^{n+1}-1}{3^n}\Rightarrow S=\frac{3^{n+1}-1}{2.3^n}\)

\(2A=1+\frac{1}{2}+\frac{1}{2^2}+.......+\frac{1}{2^{99}}\)

\(\Rightarrow2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+.......+\frac{1}{2^{99}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+.......+\frac{1}{2^{100}}\right)\)

\(A=1-\frac{1}{2^{100}}\)

\(A=\frac{2^{100}-1}{2^{100}}\)

= ba chấm

P= (1-1/1+2).(1-1/1+2+3).(1-1/1+2+3+4).....(1/1+2+3+4+...+100)

P=0

P=0 

NHẤN MÁY TÍNH LÀ RA THÔI