Question

Calculați 1 +6+62 + ... +62018.
Vă rog

Answer 1

.......................................

Answer 2

Răspuns:

$\color{CC0000}\large\boxed{\boxed{\bf S = \dfrac{6^{2019}-1}{5}}}$

Explicație pas cu pas:

Buna!

$\boxed{\bf S = 1+6+6^{2} +6^{3}+.......+6^{2018}}$

$\bf S = 6^{0}+6^{1}+6^{2} +6^{3}+.......+6^{2018}~~\bigg|\cdot 6$

$\bf 6S = 6^{0+1}+6^{1+1}+6^{2+1} +6^{3+1}+.......+6^{2018+1}$

$\boxed{\bf 6S = 6^{1}+6^{2}+6^{3} +6^{4}+.......+6^{2019}}$

$\text{\bf Scadem cele doua relatii si vom avea}$

$\bf 6S-S = 6^{1}+6^{2}+6^{3} +6^{4}+....+6^{2019}-(6^{0}+6^{1}+6^{2} +6^{3}+....+6^{2018})$

$\bf 5S = \not6^{1}+\not6^{2}+\not6^{3} +\not6^{4}+...\not~+6^{2019}-6^{0}-\not6^{1}-\not6^{2} -\not6^{3}-....-\not6^{2018}$

$\bf 5S = 6^{2019}-6^{0}$

$\bf 5S = 6^{2019}-1~~~\bigg|:5$

$\color{CC0000}\large\boxed{\boxed{\bf S = \dfrac{6^{2019}-1}{5}}}$

PS: Daca esti pe telefon, te rog sa glisezi spre dreapta pentru a vedea rezolvarea completa

==pav38==