Question

Tính:

a,A=  3.4+4.5+5.6+...+49.50

b,B=1.3+3.5+5.7+...+51.53

c,C=5.5+6.6+...+30.30

d,D=1+3+9+27+81+243+729+218+6561

Dấu"." là dấu nhân các bạn nhé giúp mk gấp nhé ai nhanh mk k 5 cái

Answer 1

a) A = 3.4 + 4.5 + 5.6 + ...+ 49.50

=> 3A = 3.4.3+4.5.3+ 5.6.3+...+49.60.3

3A = 3.4.(5-2) +4.5.(6-3) + 5.6.(7-4) + ...+ 49.60.(61-48)

3A = 3.4.5 - 2.3.4 + 4.5.6 -3.4.5 + 5.6.7-4.5.6 + 49.60.61 - 48.49.60

3A = -2.3.4 + 49.60.61

\(A=\frac{-2.3.4+49.60.61}{3}=59772\)

b) B = 1.3 + 3.5 + 5.7 + ...+ 51.53

=> 6B = 1.3.6 + 3.5.6 + 5.7.6 + ...+ 51.53.6

6B = 1.3.(5+1) + 3.5.(7-1) + 5.7.(9-3) +...+ 51.53.(55-49)

6B = 1.3.5 + 1.3 + 3.5.6 - 1.3.5 + 5.7.9 - 3.5.7 + ...+ 51.53.55 - 49.51.53

6B = 1.3 + 51.53.55

\(B=\frac{1.3+51.53.55}{6}=24778\)

Answer 2

cau c mk ko bk

d) D = 1 + 3 + 9 + 27 + 81 + 243 + 729 + 2187 + 6561

D = 3⁰+3¹+3²+3³+3⁴+3⁵+3⁶+3⁷+3⁸

=> 3D = 3¹+3²+3³+...+3⁸+3⁹

=> 3D - D = 3⁹-3⁰

2D = 3⁹-1

\(D=\frac{3^9-1}{2}=9841\)