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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
A=1/3 - 2/3^2+3/3^3 - 4/3^4+ ... - 100/3^100
=>3A=1 -2/3 +3/3^2 - 4/3^3+ ... - 100/3^99
=>4A=A+3A=1-1/3+1/3^2-1/3^3+...-1/3^99 - 100/3^100
=>12A=3.4A=3-1+1/3-1/3^2+...-1/3^98 - 100/3^99
=>16A=12A+4A=3-1/3^99-100/3^99-100/3^1...
<=>16A=3-101/3^99-100/3^100
<=>A=3/16-(101/3^99+100/3^100)/16 < 3/16
Suy ra A<3/16
![](https://rs.olm.vn/images/avt/0.png?1311)
A = 1/2.2 + 1/3.3 + ......+ 1/50.50
A < 1/1.2 + 1/2.3 +......+ 1/49.50
A < 1 - 1/2 + 1/2 - 1/3 +.......+ 1/49 - 1/50
A < 1 - 1/50
A < 49/50 < 1
=> A < 1 (đpcm)
*****k nha
Ta có: A=1/2^2+1/3^2+1/4^2+...+1/50^2<1
=> A<1/1.2+1/2.3+1/3.4+........+1/50.51
=>A< ( 1/1+ -1/2+1/2+ -1/3+1/3+ -1/4+1/4+ -1/5+1/5+.....+1/50+ -1/51)
=> A<1/1+ -1/51
=>A<51/51+ -1/51 =50/51<1
![](https://rs.olm.vn/images/avt/0.png?1311)
a, Có 2A = 4.2+2^3+2^4+...+2^21
A=2A-A=(4.2+2^3+2^4+...+2^21)-(4+2^2+2^3+...+2^20) = 4.2 + 2^21 - 4 - 2^2 = 2^21
=> A là lũy thừa cơ số 2
b, Có 3A=3^2+3^3+3^4+...+3^101
2A=3A-A=(3^2+3^3+3^4+....+3^101)-(3+3^2+3^3+....+3^100) = 3^101-3
=> 2A+3 = 3^101-3+3 = 3^101
=> A là lũy thừa của 3
k mk nha
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có: A < \(\frac{1}{1^2}+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)
Lại có: \(\frac{1}{1^2}+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}=1+\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}\)
\(=1+\left(\frac{1}{1}-\frac{1}{50}\right)\)
\(=1+\frac{49}{50}\)
Mà 1+49/50<2 nên A<1+49/50<2
Vậy A<2
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
A=1+(1/2+1/3)+(1/4+1/5+1/6+1/7)+(1/8+1/9+......+1/15)+........+ (1/2^99+1/2^99+1+........+1/2^100-1)
(Có 99 nhóm) < 1+2.1/2+2^2.1/2^2+2^3.1/2^3+.....+2^99.1/2^99
=>1+1+1+.......+1 (100 số 1)=100
=>A1+1/2+2.1/2^2+2^2.1/2^3+2^3.1/2^4+.....+2^991/2^100-1-1/2^100 =1+1/2+1/2+1/2+1/2+........+1/2-1/2^100 (100 số 1/2)
=1+100.12-1/2^100
=50+1-1/2^100>50
=>A>50 (2)
Từ (1)và (2)=>50
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{50^2}
giai thich gio hon duoc ko