Question

cho S=1\5²+1\9²+1\13²+............1\409². Chung minh S<1\12

Answer 1

4S = 4/(5x5) + 4/(9x9) + … + 1/(409x409)

Ta thấy:

4/(5x5) < 4/(3x7) = 1/3 – 1/7

4/(9x9) < 4/(7x11) = 1/7 – 1/11

…………

4/(409x409) < 4/(407x411) = 1/407 – 1/411

Mà :

4/(3x7) + 4/(7x11) + …. + 4/(407x411) = 1/3 – 1/411 = 136/411

4S < 136/411

S < 34/411 < 34/408 = 1/12

Hay  S < 1/12

Answer 2

4S = 4/(5x5) + 4/(9x9) + … + 1/(409x409)

Ta thấy:

4/(5x5) < 4/(3x7) = 1/3 – 1/7

4/(9x9) < 4/(7x11) = 1/7 – 1/11

…………

4/(409x409) < 4/(407x411) = 1/407 – 1/411

Mà :

4/(3x7) + 4/(7x11) + …. + 4/(407x411) = 1/3 – 1/411 = 136/411

4S < 136/411

S < 34/411 < 34/408 = 1/12

Hay  S < 1/12

Answer 3

4S = 4/(5x5) + 4/(9x9) + … + 1/(409x409)

Ta thấy:

4/(5x5) < 4/(3x7) = 1/3 – 1/7

4/(9x9) < 4/(7x11) = 1/7 – 1/11

…………

4/(409x409) < 4/(407x411) = 1/407 – 1/411

Mà :

4/(3x7) + 4/(7x11) + …. + 4/(407x411) = 1/3 – 1/411 = 136/411

4S < 136/411

S < 34/411 < 34/408 = 1/12

Hay  S < 1/12

Answer 4

4S = 4/(5x5) + 4/(9x9) + … + 1/(409x409)

Ta thấy:

4/(5x5) < 4/(3x7) = 1/3 – 1/7

4/(9x9) < 4/(7x11) = 1/7 – 1/11

…………

4/(409x409) < 4/(407x411) = 1/407 – 1/411

Mà :

4/(3x7) + 4/(7x11) + …. + 4/(407x411) = 1/3 – 1/411 = 136/411

4S < 136/411

S < 34/411 < 34/408 = 1/12

Hay  S < 1/12

Answer 5

4S = 4/(5x5) + 4/(9x9) + … + 1/(409x409)

Ta thấy:

4/(5x5) < 4/(3x7) = 1/3 – 1/7

4/(9x9) < 4/(7x11) = 1/7 – 1/11

…………

4/(409x409) < 4/(407x411) = 1/407 – 1/411

Mà :

4/(3x7) + 4/(7x11) + …. + 4/(407x411) = 1/3 – 1/411 = 136/411

4S < 136/411

S < 34/411 < 34/408 = 1/12

Answer 6

bạn ơi dòng đầu sai rồi nhé phải là 4S=4/(5.5)+4/(9.9)+...+4/(409.409) chứ :) :)