tính $6^{2}$ +$6^{4}$ +$6^{6}$+…+ $6^{98}$ +$6^{100}$ 30/06/2021 Bởi Peyton tính $6^{2}$ +$6^{4}$ +$6^{6}$+…+ $6^{98}$ +$6^{100}$
$Đặt$ `X` `:` `X = 6^2+6^4+6^6+…+6^98+6^100` `⇒ 6^2×X = 6^4+6^6+6^8+…+6^100+6^102` `⇒ 6^2×X-X = 35×X = 6^102−6^2` `⇒ X = (6^102−6^2)/35` $#JAW#$ Bình luận
Đặt `A=6^2 + 6^4 + 6^6 + …. + 6^{98}+6^{100}` `6^2A = 6^2.(6^2 + 6^4 + 6^6 + …. + 6^{98}+6^{100})` `36A=6^4 + 6^6 + 6^8+ …. + 6^{100}+6^{102}` `36A – A = (6^4 + 6^6 + 6^8+ …. + 6^{100}+6^{102}) – (6^2 + 6^4 + 6^6 + …. + 6^{98}+6^{100})` `35A= 6^{102} – 6^2` `A= {6^{102}-6^2}/35` Bình luận
$Đặt$ `X` `:`
`X = 6^2+6^4+6^6+…+6^98+6^100`
`⇒ 6^2×X = 6^4+6^6+6^8+…+6^100+6^102`
`⇒ 6^2×X-X = 35×X = 6^102−6^2`
`⇒ X = (6^102−6^2)/35`
$#JAW#$
Đặt `A=6^2 + 6^4 + 6^6 + …. + 6^{98}+6^{100}`
`6^2A = 6^2.(6^2 + 6^4 + 6^6 + …. + 6^{98}+6^{100})`
`36A=6^4 + 6^6 + 6^8+ …. + 6^{100}+6^{102}`
`36A – A = (6^4 + 6^6 + 6^8+ …. + 6^{100}+6^{102}) – (6^2 + 6^4 + 6^6 + …. + 6^{98}+6^{100})`
`35A= 6^{102} – 6^2`
`A= {6^{102}-6^2}/35`