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VA IMPLOOOOR. REEEEPEDEE. DAU COROANAAA PROMIIIIT. VAAA ROOOOG MUUULT. AMMMM NEVOOOIE URGEEENT. VAA IMPLOOOR​

VA IMPLOOOOR REEEEPEDEE DAU COROANAAA PROMIIIIT VAAA ROOOOG MUUULT AMMMM NEVOOOIE URGEEENT VAA IMPLOOOR class=

Răspuns :

Răspuns:

Explicație pas cu pas:

a)

1/1*2 = 1 - 1/2

1/2*3 = 1/2 - 1/3

.....

1/99*100 = 1/99 - 1/100

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1/1*2 + 1/2*3 + ...+ 1/99*100 = 1 - 1/2 + 1/2 - 1/3 + ...+ 1/99 - 1/100 = 1 - 1/100 = 99/100 = 0,99

0,5 < 0,99 < 1 adevarat

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b)

2/1*3 = 1 - 1/3

2/3*5 = 1/3 - 1/5

2/5*7 = 1/5 - 1/7

........

2/99*101 = 1/99 - 1/101

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2/1*3 + 2/3*5 + 2/5*7 + ...+ 2/99*101

= 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ...+ 1/99 - 1/101

= 1 - 1/101 = 100/101

100/101 + 2/100*101 = 100*100/100*101 + 2/100*101 = 10002/ 10100 < 1

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