Răspuns:
Explicație pas cu pas:
c)
11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99 = 495
495/33 = x/2
x = 2*495/33 = 30
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b)
1 + 3 + 5 + .... + 2005
a1 = 1; an = 2005; r = 2
2005 = 1 + (n - 1)*2 = 1 + 2n - 2 = 2n - 1
2n = 2006
n = 1003
1 + 3 + 5 + .... + 2005 = 1003*(1 + 2005)/2 = 1003*2006/2= 1003*1003
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2 + 4 + 6 + ..... + 2006
a1 = 2; an = 2006; r = 2
2006 = 2 + (n - 1)*2 = 2 + 2n - 2 = 2n
n = 2006 : 2 = 1003
2 + 4 + 6 + .... + 2006 = 1003*(2 + 2006)/2 = 1003*2008/2 = 1003*1004
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1003*1003/1003*1004 = 1003/x
1003/1004 = 1003/x
x = 1003*1004/1003 = 1004
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d)
201 + 202 + ....+ 400
a1 = 201; an = 400; r = 1
400 = 201 + (n - 1)*1 = 201 + n - 1 = 200 + n
n = 200
201 + 202 + .... + 400 = 200*(201 + 400)/2 = 100*601
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101 + 102 + .... + 200
a1 = 101; an = 200; r = 1
200 = 101 + (n - 1)*1 = 101 + n - 1 = 100 + n
n = 200 - 100 = 100
101 + 102 + .... + 200 = 100*(101 + 200)/2 = 50*301
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100*601/50*301 = 601 x/50
x = 100/301
