Question

1+6+6 la puterea 2+......+6 la puterea 2018
Repede va rog!

Answer 1

$\red{\boxed{ \: \bf S = \dfrac{6^{2019}-1}{5} \: }}$

Bună !

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

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

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

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

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

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

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

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

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

$\pink{\boxed{ \: \bf S = \dfrac{6^{2019}-1}{5} \: }}$

$==pav38==$