Question

Cum rezolv?
$s= ( \frac{1}{1 + 2} + \frac{1}{1 + 2 + 3} + \frac{1}{1 + 2 + 3 + 4} + ... + \frac{1}{1 + 2 + ... + 10} ) \times 44$
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Answer 1

Răspuns:

Observi ca la numitor sunt sume gauss

1+2=2*3/2   1/1+2=2/2*3

1+2+3=3*4/2   1/(1+2+3)=2/3*4

1+2+3+4=4*5/2    1/(1+2+3+4)=2/4*5

..............................................................................................

1+2+3+...=10=10*11/2         1/(1+2+3+...+10)=2/10*11

2/3*4+2/4*5+....2/10*11=

2(1/3*4+1/4*5+,,,,+1/10*11)=

2[1/3-1/4+1/4-1/5+...+1/10-1/11)= termenii intermediari se reduc si ramane

2(1/3-1/11)=

2(11-1)/3*11=

2*10/3*11=20/3*11

s=20/3*11*44=20/3*44/11=

20/3*4=80/3

Explicație pas cu pas: