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CMR :1/(5+1)+2/(5^2+1)+4/(5^4+1)+⋯+1024/(5^1024+1) <1/4
1. (1+1/2).(1+1/2^2).(1+1/2^3)....(1+1/2^100) < 3
2. 1/(5+1)+2/(5^2+1)+4/(5^4+1)+...+ 1024/(5^1024+1) <1/4
3. 3/(1!+2!+3!)+4/(2!+3!+4!)+...+100/(98!+99!+100!) <1/2
1.tính tổng
1+2+3+5+8+.....+55
1+4+16+.....+1024
Bài 1: tìm x
a) 2^2x.2^4=1024
b) 2.3^x=10.3^12+8.27^4
c) 5^8.25^x+1=5^17
d) 3^x-1+3^x-4=28.243
e) (2x-4)^5=(2x-4)^3
Tính nhanh:
a, A = 1 + 2 + 4 + 8 +...+ 1024
b, B = 1 + 5 + 25 + 125 + ... + 15625
c, C = 1 / 1 .2 + 1 / 2 .3 + 1 / 3 .4 + .. + 1 / 2015 .2016
d, D = 10 / 1 . 3 + 10 / 3 . 5 + 10 / 5 . 7 + ... + 10 / 2013 . 2015
lam vay co duoc ko
1/2+1/4+1/8+... +1/512+1/1024=1-1/2+1/2-1/4+...+1/512-1/1024=1-1/1024=1/1023
\(A=\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{4}\right)+\left(1-\frac{1}{8}\right)+...+\left(1-\frac{1}{1024}\right)\)
\(B=4.5^{100}.\left(\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+...+\frac{1}{5^{100}}\right)+1\)
Tính: \(M=\frac{1}{2}+\frac{2}{4}+\frac{3}{8}+\frac{4}{16}+\frac{5}{32}+...+\frac{10}{1024}\)
1024:64+[140:(38+2/5)-1/3]
2/5 là 2 mũ 5
1/3 là 1 mũ 3