Chứng tỏ 

a, 1/2-1/4+1/8-1/16+1/32-1/64<1/3

b, 1/3-2/3^2+3/3^3-4/3^4+...+99/3^99-100/3^100<3/16

c, 1/2.3/4.5/6...9999/10000<1/100

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

CMR:

a)1/10^2 +1/11^2+1/12^2+...+1/100^2 >3/4

b)1/2^2+1/3^2+1/4^2+...+1/100^2<99/100

c)1/2^2+1/3^2+1/4^2+...+1/100^2<3/4

CMR:

a)1/2-1/4+1/8-1/16+1/32-1/64<1/3

b)1/3 - 2/3^2 + 3/3^3 - 4/3^4 +...+ 99/3^99 -100/3^100 < 3/16

cmr

a) 1/2 -1/4+1/8-1/16+1/32-1/64 <1/3

b) 1/3-2/3^2+3/3^3-4/3^4+...+99/3^99-100/3^100<3/16

Chưng tỏ

a, S= 1/2^2+1/3^2+...+1/9^2 

Chứng tỏ 2/5<S<8/9

b, 1/2-1/4+1/8-1/16+1/32-1/64<1/3

c, 1/3-2/3^2+3/3^3-4/3^4+...+99/3^99-100/3^100<3/16

chứng minh

a) 1/3^2+2/3^3+3/3^4+...+100/3^101<1/4

b) 1/3-2/3^2+3/3^3-4/3^4+...+99/3^99-100/3^100<3/16

c) 1/31+1/32+...+1/60=1/1x2+1/3x4+1/5x6+...+1/59x60

d) 1x3x5x7x...x49=26/2x27/2x28/2x...x50/2

Chứng minh rằng:

a) 1/2-1/4+1/8-1/16+1/32-1/64<1/3

b) 1/3-2/3^2+3/3^3-3/3^4+...+99/3^99-100/3^100<3/16

Chứng minh rằng:

a,A=1/2+1/2^2+1/2^3+.+1/2^2<1

b,B=1/3+1/3^2+1/3^3+...+1/3^n<1/2

c,B=1/2-1/2^2+1/2^3-1/2^4+...+1/2^2015-1/2^2016<1/3

d,D=1/3+2/3^2+3/3^3+4/3^4+...+100/3^100<3/4