Question

[Trương Lê Quỳnh Anh]

Tính tổng:

S = (1/2)+(3/4)+(7/8)+(15/16)+...+(127/128)-6

HELP ME!!!

Answer 1

[09031993inyourarea]

S₁ = \(\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+...+\frac{127}{128}\)

2S₁ = 1 + \(\frac{3}{2}+\frac{7}{4}+\frac{15}{8}+\frac{31}{16}+\frac{63}{32}+\frac{127}{64}\)
2S₁ - S₁ = S₁ = 1 + (1 + 1 + 1 + 1 + 1 + 1) - \(\frac{127}{128}\)= 6 + \(\frac{1}{128}\)
=> S = S₁ - 6 = 6 + \(\frac{1}{128}\)- 6 = \(\frac{1}{128}\)

Answer 2

[✎✰ ๖ۣۜLαɗσηηα ༣✰✍]

\(S=\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+\frac{31}{32}+\frac{63}{64}+\frac{127}{128}-6\)

\(S=\frac{1}{2}+\left(\frac{3}{4}+\frac{7}{8}\right)+\left(\frac{15}{16}+\frac{31}{32}\right)+\left(\frac{63}{64}+\frac{127}{128}\right)-6\)

\(S=\frac{1}{2}+\frac{13}{8}+\frac{61}{32}+\frac{253}{128}-6\)

\(S=\frac{64}{128}+\frac{208}{128}+\frac{244}{128}+\frac{253}{128}-6\)

\(S=\frac{769}{128}-6\)

\(S=\frac{769}{128}-\frac{768}{128}\)

\(S=\frac{1}{128}\)

hok tốt!!