A=1/2 - 1/4+1/8-1/16+1/32-1/64+....+1/2(99)-1/2(100)

Tính A

Chứng minh A < 1/3

* chú ý : 1/2(99) là 1/2 mũ 99; 1/2(100) là 1/2 mũ 100

Mn giúp e vs ạ

1.Chứng minh rằng a)1/2-1/4+1/8-1/16+1/32-1/64<1/3 b)1/3-2/3^2+3/3^3-4/3^4+...+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

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

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 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

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

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

b) 1/3 - 2/3² + 3/3³ - 4/3⁴ +...+ 99/3⁹⁹ - 100/3¹⁰⁰ < 3/16