Question

4 Calculați 1 + 6 + 6² + ... + 6²⁰¹⁸​

Answer 1

Bună!

$S=1 + 6 + 6^{2} + ... + 6^{2018} /*6\\6S=6 + 6^{2} +6^{3} ... + 6^{2019}\\----------------- (adunare)\\7S=(1 + 6 + 6^{2} + ... + 6^{2018})+6^{2019}-1/-S\\7S-S=6^{2019}-1\\6S=6^{2019}-1\\S=\frac{6^{2019}-1}{6}$