Tính tích
A=\(\frac{3}{4}x\frac{8}{9}x\frac{15}{16}x....x\frac{2499}{2500}\)
Những câu hỏi liên quan
Kí hiệu [x] là số nguyên lớn nhất không vượt quá x.
Cho A= \(\frac{3}{4}+\frac{8}{9}+\frac{15}{16}+...+\frac{2499}{2500}\)
Vậy [A]=???
tim x biet
a)\(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}...\frac{2499}{2500}\)
b) \(\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}...\frac{50^2}{49.51}\)
Tính:
\(\frac{3}{4}+\frac{8}{9}+\frac{15}{16}+\frac{24}{25}+...+\frac{2499}{2500}\)
CMR;\(\frac{3}{4}+\frac{8}{9}+\frac{15}{16}+.....+\frac{2499}{2500}>48\)
Đặt \(B=\frac{3}{4}+\frac{8}{9}+\frac{15}{16}+...+\frac{2499}{2500}\)
Chúc bạn học tốt!
chứng minh:c=\(\frac{3}{4}+\frac{8}{9}+\frac{15}{16}+...+\frac{2499}{2500}\)>48
Kí hiệu [x] là số nguyên lớn nhất không vượt quá x
Cho A =\(\frac{3}{4}+\frac{8}{9}+\frac{15}{36}+...+\frac{2499}{2500}\)
Vậy [A] = ... ?
Cho B=\(\frac{3}{4}+\frac{8}{9}+\frac{15}{16}+...+\frac{2499}{2500}\)
CMR:B>48
\(B=\frac{3}{4}+\frac{8}{9}+\frac{15}{16}+...+\frac{2499}{2500}\)
\(\Rightarrow B=\left(1-\frac{1}{4}\right)+\left(1-\frac{1}{9}\right)+\left(1-\frac{1}{16}\right)+...+\left(1-\frac{1}{2500}\right)\)
\(\Rightarrow B=\left(1-\frac{1}{2^2}\right)+\left(1-\frac{1}{3^2}\right)+\left(1-\frac{1}{4^2}\right)+...+\left(1-\frac{1}{50^2}\right)\)
\(\Rightarrow B=\left(1+1+1+...+1\right)-\left(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{50^2}\right)\) (có 49 số 1)
\(\Rightarrow B=49-\left(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{50^2}\right)\)
Ta có: \(\frac{1}{2^2}< \frac{1}{1.2};\frac{1}{3^2}< \frac{1}{2.3};\frac{1}{4^2}< \frac{1}{3.4};...;\frac{1}{50^2}< \frac{1}{49.50}\)
\(\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{50^2}< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)
\(\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{50^2}< 1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}\)
\(\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{50^2}< 1-\frac{1}{50}\)<1
\(\Rightarrow-\left(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{50^2}\right)>-1\)
\(\Rightarrow49-\left(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{50^2}\right)>49-1\)
\(\Rightarrow B>48\)
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chứng minh rằng:
\(\frac{3}{4}+\frac{8}{9}+\frac{15}{16}+...+\frac{2499}{2500}>48\)
Tính
A=\(\frac{8}{9}+\frac{15}{16}+\frac{24}{25}+...+\frac{2499}{2500}\)
a=8/9+15/16+24/25+....+2499/2500
a=(1-1/9)+(1-1/16)+(1-1/25)+....+(1-1/2500)
a=1-1/9+1-1/16+1-1/25+....+1-1/2500
a=(1+1+...+1)-(1/9+1/16+1/25+....+1/2500)
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