[tex]( - 2) \times (2) ^{2} \times ( - 2) { }^{3} \times ( - 2) { }^{4} \times ..... \times (

May 2021 2 49 Report

[tex]( - 2) \times (2) ^{2} \times ( - 2) { }^{3} \times ( - 2) { }^{4} \times ..... \times ( - 2) {}^{100} \div {4}^{2525} [/tex]
Cine poate sa îmi facă problema aceasta folosind suma lui gauss?

pav38

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Răspuns:

$\large \bf( - 2)^{1} \cdot ( - 2)^{2} \cdot( - 2)^{3} \cdot ( - 2)^{4} \cdot ....\cdot ( - 2)^{100} : {4}^{2525} =$

$\large \bf( - 2)^{1 + 2 + 3 + 4 + .... + 100} : {4}^{2525} =$

Aplicam suma lui Gauss pentru a afla exponentul lui (-2)

100 • (100 + 1) : 2 = 50 • 101 = 5050

$\large \bf( - 2)^{5050} : {4}^{2525} =$

$\large \bf( - 2)^{5050} : (2^{2})^{2525} =$

$\large \bf 2^{5050} : 2^{2 \cdot 2525} =$

$\large \bf 2^{5050} : 2^{5050} =$

$\large \bf 2^{5050 - 5050}={2}^{0} = \boxed{ \bf 1}$

#copaceibrainly

iuliaplop06 salut

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