B=1/3+1/32+1/33+...+1/32005
3B = 1+1/3+1/32+...+1/32004
3B-B = 1-1/32005
2B = 1-1/32005
B = (1-1/32005)/2
Mà 1-1/32005 < 1
=> (1-1/32005)/2 < 1/2
hay 1/3+1/32+1/33+...+1/32005 < 1/2
so sanh S=1/30+1/31+1/32+....+1/59+1/60 voi 1/2
Chứng minh rằng:
A = 1/3 + 1/32 + 1/33 + ..........+ 1/399 < 1/2
B = 3/12x 22 + 5/22 x 32 + 7/32 x 42 +............+ 19/92 x 102 < 1
C = 1/3 + 2/32 + 3/33 + 4/34 +.........+ 100/3100 ≤ 0
cho A=(1/22-1)+(1/32-1)+...................+(1/20182-1) voi B =-1/2
so sanh A va B
A=1/1*2+1/2*3+1/3*4+......+1/99*100 so sanh voi 1
A=1/4+1/42+1/43+.....+1/499
a) Rut gon A
b) So sanh A voi 1/3
\(choB=\left(\frac{1}{2^2}-1\right).\left(\frac{1}{3^2}-1\right).\left(\frac{1}{4^2}-1\right)....\left(\frac{1}{100^2}-1\right)\)
so sanh B voi \(-\frac{1}{2}\)
so sanh a=(1/2-1)(1/3-1)(1/4-1)...(1/10-1)voi -1/9
so sanh
1/3+1/3^2+1(3^3)+...+1/3^2011+1/3^2012 voi 1/2
tinh A/B, biet
A=1/2*32+1/3*33+1/4*34+...+1/n*(n+30)+...+1/1973*2003
B=1/2*1974+1/3*1975+1/4*1976+...+1/n*(n+1972)+...+1/31*2003.
