a)\(=\left(\frac{-3}{13}-\frac{10}{13}\right)+\left(\frac{7}{12}+\frac{5}{12}\right)\)

\(=-1+1=0\)

b)=

=2*(1/6+1/12+1/20+...+1/380)

=2*(1/2*3+1/3*4+1/4*5+...+1/19*20)

=2*(1/2-1/3+1/3-1/4+1/4-1/5+...+1/19-1/20)

=2*(1/2-1/20)

=2*(10/20-1/20)

=2*9/20

=18/20

=9/10

A/2=(1/3+1/6+1/10+1/15+...+1/171+1/190)/2

=1/6+1/12+1/20+1/30+...+1/342+1/380

=1/2.3+1/3.4+1/4.5+1/5.6+....+1/18.19+1/19.20

=1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 +....+ 1/18 - 1/19 + 1/19 - 1/20

=1/2 - 1/20 = 10/20 - 1/20 = 9/20

=> A = 9/20 .2 = 18/20=9/10

6³⁰ . 6¹⁰ = 6^(30+10) = 6⁴⁰

Vậy tích trên bằng 6⁴⁰

6³⁰.6¹⁰=6^(30+10)=6⁴⁰

Tích trên là 6⁴⁰ bạn nhé

\(A=6^3+6^6+6^9+...+6^{27}\)

\(6^3.A=6^6+6^9+6^{12}+...+6^{30}\)

\(216A-A=215A=6^{30}-6^3\)

\(\Rightarrow A=\frac{6^{30}-6^3}{215}\)

6³+6⁶+6⁹+...+6²⁷

Đặt A=6³+6⁶⁺6⁹+...+6²⁷

6A=6³.(6³+6⁶+6⁹+...+6²⁷)

6A=6⁶+6⁹+6¹²+...+6³⁰

6A-A=6³⁰-6³

5A=6³⁰-6³

A=(6³⁰-6³)/5

A = 1 + 2 + 3 + ... + n

A = (n + 1).n : 2

B = 1 + 3 + 5 + ... + (2n - 1)

B = (2n - 1 + 1).[(2n - 1 - 1) : 2 + 1]

B = 2n[(2n - 2) : 2 + 1]

B = 2n[2(n - 2) : 2 + 1]

B = 2n(n - 2 + 1)

B = 2n(n - 1)

C = 2 + 4 + 6 + ... + 2n

C = (2n + 2)[(2n - 2) : 2 + 1]

C = 2(n + 1)[2(n - 1) : 2 + 1]

C = 2(n + 1)(n - 1 + 1)

C = 2(n + 1)n

=(1-2)-(3-4)+(5-6)-(7-8)+...+(2021-2022)-2023
=(-1)-(-1)+(-1)-...+(-1)-2023
=0-2023
=-2023

Số số hạng:(200-1)+1=200

Tổng:200(200+1):2=20100

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