Question

cho c=3/5+11/13+...+19799/19801

chứng minh c>98

Answer 1

mình cũng đang bí bài này

Answer 2

C=3/(1²+2² )+ 11/(2²+3²⁾+....+19799/(99²+100²⁾

Suy ra C có 99 số .

C=(1-2/5)+(1-2/13)+...+(1-2/19801)

C=99-(2/5+2/13+...+2/19801)

bây giờ chúng ta phải chứng minh biểu thức trong ngoặc nhỏ hơn 1.

Xét B=2/5+2/13+...+2/19801

B<2/4+2/12+...+2/19800

B<1/2+1/6+...+1/9900

B<1/1x2+1/2x3+...+1/99x100

B<1-1/100<1

Vậy B < 1 thì C> 99-1=98

 

Answer 3

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