Đặt \(\frac{1}{2^2}+\frac{1}{2^4}+\frac{1}{2^6}+...+\frac{1}{2^{100}}\)là A
Ta có :A = \(\frac{1}{2}\left(1-\frac{1}{2^{100}}\right)\)
Vì 1-...
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cho b= \(\frac{1}{2^2}+\frac{1}{2^4}+\frac{1}{2^6}+........+\frac{1}{2^{98}}+\frac{1}{2^{100}}\)
chứng minh b< \(\frac{1}{3}\)
chứng minh rằng : \(\frac{1}{7^2}-\frac{1}{7^4}+\frac{1}{7^6}-...+\frac{1}{7^{98}}-\frac{1}{7^{100}}< \frac{1}{50}\)
Cho 3 số a;b;c thỏa mãn a.b.c1Chứng minhfrac{1}{ab+a+1}+frac{b}{bc+b+1}+frac{1}{abc+bc+b}12)CHứng tỏ rằnga1-frac{1}{2}-frac{1}{2^2}-frac{1}{2^3}-....-frac{1}{2^{10}}frac{1}{2^{11}}b1-frac{1}{2^2}-frac{1}{3^2}-frac{1}{4^2}-...-frac{1}{100^2}frac{1}{100}cleft(frac{1}{2^2}-1right).left(frac{1}{3^2}-1right).left(frac{1}{4^2}-1right)...left(frac{1}{100^2}-1right)
Đọc tiếp
Cho 3 số a;b;c thỏa mãn a.b.c=1
Chứng minh
\(\frac{1}{ab+a+1}+\frac{b}{bc+b+1}+\frac{1}{abc+bc+b}=1\)
2)
CHứng tỏ rằng
\(a=1-\frac{1}{2}-\frac{1}{2^2}-\frac{1}{2^3}-....-\frac{1}{2^{10}}>\frac{1}{2^{11}}\)
\(b=1-\frac{1}{2^2}-\frac{1}{3^2}-\frac{1}{4^2}-...-\frac{1}{100^2}>\frac{1}{100}\)
\(c=\left(\frac{1}{2^2}-1\right).\left(\frac{1}{3^2}-1\right).\left(\frac{1}{4^2}-1\right)...\left(\frac{1}{100^2}-1\right)
Tính :
\(A=\frac{1\cdot98+2\cdot97+3\cdot96+......+98\cdot1}{1\cdot2+2\cdot3+3\cdot4+......+98\cdot99}\)
\(B=\frac{100-\left(1+\frac{1}{2}+\frac{1}{3}+..........+\frac{1}{100}\right)}{\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+.........+\frac{99}{100}}\)
chứng minh rằng \(\frac{1}{7^2}-\frac{1}{7^4}+\frac{1}{7^6}-\frac{1}{7^8}+...+\frac{1}{7^{98}}-\frac{1}{7^{100}}<\frac{1}{50}\)
ai nhanh minh k cho
\(B=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}{\frac{99}{1}+\frac{98}{2}+\frac{97}{3}+....+\frac{1}{99}}\)
Chứng minh rằng:
\(A=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< 1\) \(B=\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+\frac{4}{3^4}+...+\frac{100}{3^{100}}+\frac{101}{3^{101}}< \frac{3}{4}\)
1/ Tínha) P1+frac{1}{2}left(1+2right)+frac{1}{3}left(1+2+3right)+frac{1}{4}left(1+2+3+4right)+...+frac{1}{16}left(1+2+3+...+16right)b) Cho a+b+c2010và frac{1}{a+b}+frac{1}{b+c}+frac{1}{c+a}frac{1}{3}Tính Sfrac{a}{b+c}+frac{b}{c+a}+frac{c}{a+b}2/ Tìm x biếtfrac{1}{4}cdotfrac{2}{6}cdotfrac{3}{8}cdotfrac{4}{10}...frac{30}{62}cdotfrac{31}{64}2^x3/ Tìm a_1;a_2;a_3;...;a_{100}biết frac{a_1-1}{100}frac{a_2-2}{99}frac{a_3-3}{98}...frac{a_{100}-100}{1}và a_1+a_2+a_3+...+a_{100}10100
Đọc tiếp
1/ Tính
a) \(P=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+\frac{1}{4}\left(1+2+3+4\right)+...+\frac{1}{16}\left(1+2+3+...+16\right)\)
b) Cho \(a+b+c=2010\)và \(\frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a}=\frac{1}{3}\)
Tính \(S=\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\)
2/ Tìm x biết
\(\frac{1}{4}\cdot\frac{2}{6}\cdot\frac{3}{8}\cdot\frac{4}{10}...\frac{30}{62}\cdot\frac{31}{64}=2^x\)
3/ Tìm \(a_1;a_2;a_3;...;a_{100}\)biết \(\frac{a_1-1}{100}=\frac{a_2-2}{99}=\frac{a_3-3}{98}=...=\frac{a_{100}-100}{1}\)và \(a_1+a_2+a_3+...+a_{100}=10100\)
Cho B=\(\frac{1}{2}+\left(\frac{1}{2}\right)^2+\left(\frac{1}{2}\right)^3+....+\left(\frac{1}{2}\right)^{98}+\left(\frac{1}{2}\right)^{99}\)
Chứng minh B<1