Question

Va rog daca ma puteti ajuta cu ex 10 / e,f,d . Multumesc

Answer 1

Răspuns:

Explicație pas cu pas:

d)

2 + 4 + 6 + ......+ 2018

2018 = 2 + (n - 1)*2 = 2 + 2n - 2 = 2n

n = 2018 : 2 = 1009 termeni in suma

2 + 4 + 6 + ....+ 2018 = 1009*(2 + 2018)/2 = 1009 * 2020/2 = 1009*1010

1009*1010 + 1010 = 1010 (1009 + 1) = 1010*1010 = patrat perfect

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e)

3 + 6 + 9 + 12 + .... + 864

864 = 3 + (n - 1)*3 = 3 + 3n - 3 = 3n

n = 864 : 3 = 288

3 + 6 + 9 + 12 + ..... + 864 = 288*(3 + 864)/2 = 144*867 = 124848

124848 + 41616 = 41616 (3 + 1) = 41616*4 = 204*204*2*2 = 408*408 patrat perfect

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f)

1 + 3 + 5 + 7 + ....+ 2017

2017 = 1 + (n - 1)*2 = 1 + 2n - 2 = 2n - 1

2n = 2017 + 1 = 2018

n = 2018 : 2 = 1009

1 + 3 + 5 + 7 + .... + 2017 = 1009*(1 + 2017)/2 = 1009*2018/2 = 1009*1009

3*1009*1009 - 1009*2018 = 3*1009*1009 - 1009*2*1009 = 1009*1009 patrat perfect