\(M=1+3^2+3^4+3^6+...+3^{112}\)

\(\Rightarrow3M=3+3^3+3^5+3^7+...+3^{113}\)

\(\Rightarrow3M+M=1+3^2+3^4+3^5+...+3^{113}\)

\(\Rightarrow4M=\dfrac{3^{113+1}-1}{3-1}\)

\(\Rightarrow M=\dfrac{3^{114}-1}{2.4}=\dfrac{3^{114}-1}{8}\)

\(M=\dfrac{6}{5}+\dfrac{3}{2}\left(\dfrac{2}{35}+\dfrac{2}{63}+...+\dfrac{2}{9603}+\dfrac{2}{9999}\right)\)

\(=\dfrac{6}{5}+\dfrac{3}{2}\left(\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{97}-\dfrac{1}{99}+\dfrac{1}{99}-\dfrac{1}{101}\right)\)

\(=\dfrac{6}{5}+\dfrac{3}{2}\cdot\dfrac{96}{505}=\dfrac{150}{101}\)

CHỊU THÔI

mình cũng muốn giải bài toán í

M=3+3²+3³+...+3ⁿ

=>3M=3²+3³+3⁴+...+3ⁿ⁺¹

=>3M-M=3ⁿ⁺¹-3

=>2M=3ⁿ⁺¹-3

=>M=\(\frac{3^{n+1}-3}{2}\)

\(N=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^n}\)

=>3N\(=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{n-1}}\)

=>3N-N=\(1-\frac{1}{3^n}\)

=>2N=\(1-\frac{1}{3^n}\Rightarrow N=\frac{1-\frac{1}{3^n}}{2}\)

help me

+) M = 1+(-2)+3+(-4)+...+2001+(-2002) = [1+(-2)]+[3+(-4)]+...+[2001+(-2002)]

=-1-1-...-1 = -1.1001 (2002 chữ số 1)

M=-1001

+) M = 1+2+(-3)+4-...-1999+2000 = [1+2+(-3)]+[4+5+(-6)]+...+(-1999+2000)

= 0+0+...+1

M=1

cau hoi nay ai chang lam dc

học vs hành, bỏ đi, bỏ đi, ra cái đề câu mô cụng hỏi rk hk mần chi

\(M=1+3+3^2+3^3+...+3^{20}+3^{21}\)

\(\implies 3M=3+3^2+3^3+3^4+...+3^{21}+3^{22}\)

\(\implies 3M-M=(3+3^2+3^3+3^4+...+3^{21}+3^{22})-(1+3+3^2+3^3+...+3^{20}+3^{21})\)

\(\implies 2M=3^{22}-1\)

\(\implies M=\frac{3^{22}-1}{2}\)

_Học tốt_

\(M=1+3+3^2+3^3+....+3^{20}+3^{21}\)

\(\Rightarrow3M=3+3^2+3^3+3^4+.....+3^{21}+3^{22}\)

\(\Rightarrow3M-M=\left(3+3^2+3^3+....+3^{22}\right)-\left(1+3+3^2+....+3^{21}\right)\)

\(\Rightarrow2M=3^{22}-1\)

\(\Rightarrow M=\frac{3^{22}-1}{2}\)

Bn hc trường nào zậy??

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