Question

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Answer 1

Răspuns:

Explicație pas cu pas:

2^n+3*5^n + 10^n = 2^3*2^n*5^n + 10^n = 8*10^n + 10^n = 9*10^n

10^n + 2^n*5^n+1 = 10^n + 5*2^n*5^n = 10^n + 5*10^n = 6*10^n

9*10^n / 6*10^n = 9/6 = 3/2

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3 + 9 + 15 + ....+ 3003

a1 = 3; an = 3003; r = 6

3003 = 3 + 6(n - 1) = 3 + 6n - 6 = 6n - 3

6n = 3003 + 3 = 3006

n = 3006 : 6 = 501

S = 501*(3 + 3003)/2 = 501*3006/2 = 501*1503

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2 + 6 + 10 + ...+ 2002

a1 = 2; an = 2002; r = 4

2002 = 2 + 4(n - 1) = 2 + 4n - 4 = 4n - 2

4n = 2002 + 2 = 2004

n = 2004 : 4 = 501

S = 501*(2 + 2002)/2 = 501*2004/2 = 501*1002

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501*1503 / 501*1002 = 1503/1002 = 3*501/2*501 = 3/2

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3/2 = 3/2