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Question

So sánh

M= 3¹+ 3 ²+3³ + .....3¹⁰⁰

M= 3¹⁰¹

kudo shinichi · Accepted Answer

$M=3+3^2+3^3+...+3^{100}$

$\Rightarrow3M=3^2+3^3+3^4+...+3^{100}+3^{101}$

$3M-M=\left(3^2+3^3+3^4+...+3^{100}+3^{101}\right)-\left(3+3^2+3^3+...+3^{100}\right)$

$2M=3^{101}-3$

$\Rightarrow M=\frac{3^{101}-3}{2}< 3^{101}$

Câu trả lời:

$M=3+3^2+3^3+...+3^{100}$

$\Rightarrow3M=3^2+3^3+3^4+...+3^{100}+3^{101}$

$3M-M=\left(3^2+3^3+3^4+...+3^{100}+3^{101}\right)-\left(3+3^2+3^3+...+3^{100}\right)$

$2M=3^{101}-3$

$\Rightarrow M=\frac{3^{101}-3}{2}< 3^{101}$

nguyen duc thang · Answer

M = 3¹ + 3² + ... + 3¹⁰⁰

=> 3M = 3² + 3³ + ... + 3¹⁰¹

=> 3M - M = ( 3² + 3³ + ... + 3¹⁰¹) - ( 3¹ + 3² + ... + 3¹⁰⁰ )

2M = 3¹⁰¹ - 3¹

=> M = $\frac{3^{101}-1}{2}$< 3¹⁰¹ = M₂