Question

Suma

$\sqrt{1 + 3 + 5 + 7 + ... + 2015 + 2017 + 2019}$
Calculati suma asta va rog!!!!
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Answer 1

Răspuns:

1010

Explicație pas cu pas:

mai intai aflam numarul de termeni,  2n-1=2019, ⇒2n=2020, ⇒n=1010.

Sunt mai multe moduri de a calcula suma, eu voi incerca acum astfel:

fiecare termen k il voi scrie ca (k+1)-1, de exemplu 7=8-1,...

avem 1010 termeni, vom obtine 1010 de -1

1+3+5+7+...+2015+2017+2019=2-1+4-1+6-1+8-1+....+2016-1+2018-1+2020-1=(2+4+6+8+....+2016+2018+2020)- 1010= 2·(1+2+3+4+...+1010) - 1010 =

=2·1010·1011/2 - 1010=1010·1011-1010=1010·(1011-1)=1010·1010=1010²

Deci √(1010²)=1010

Answer 2

=(√ 1+2+3+.....2019 ) -(√ 2+4+6+.....2018)

= √( 2019×2020/2) -√2×( 1+2+3+.....1009)

= √ ( 2019 × 1010) - √ 2× 1009×1010 /2 =

= √ 2019×1010 − √ 1009×1010 =

√ 1010× √ ( 2019 − 1009) =

√ 1010 × √1010 = 1010