a)

C = 1 − 2 + 3 − 4 + ... + 97 − 98 + 99 − 100 = 1 − 2 + 3 − 4 + ... + 97 − 98 + 99 − 100 = − 1 + − 1 + ... + − 1 + − 1 = − 1.50 = − 50.

b)

B = 1 − 2 − 3 + 4 + 5 − 6 − 7 + ... + 97 − 98 − 99 + 100 = 1 − 2 + − 3 + 4 + 5 − 6 + ... + 97 − 98 + − 99 + 100 = − 1 + 1 + − 1 + ... + − 1 + 1 = − 1 + 1 + − 1 + 1 + ... + − 1 + 1 − 1 = 0 + 0 + ... + 0 − 1 = − 1.

101 + 100 + ... + 2 + 1 = 101x102/2 = 101x51 = 5151 
101 - 100 + 99 - .. + 1 = ( 101 -100 ) + ( 99 - 98 ) + ... + ( 3 - 2 ) + 1 = 1 + 1 + 1 + ... + 1 ( 51 số ) = 51 
suy ra C = 5151/51 = 101 

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3737x43 - 4343x36 = 37x101x43 - 43x101x36 = 43x101 = 4343 
2 + 4 + 6 +... + 100 = 2x( 1 + 2 + ... + 50 ) = 2x50x51/2 = 50x51 = 2550 

vậy D = 4343/2550 

b,D = 4343/2550

 Khó vãi 

ua sao khong thay

Số số hạng là 
   (100-2):2+1= 50 số
 Tổng là 
   (100+2)x50:2=2550

\(A=2^3\left(1^3+2^3+3^3+...+50^3\right)\)

Đặt \(S=1^3+2^3+3^3+...+50^3\)

Ta có: \(n^3=\left(n-1\right)n\left(n+1\right)+n\)

Áo dụng ta được: 

\(1^3=0+1\)

\(2^3=1.2.3+2\)

\(3^3=2.3.4+3\)

...

\(50^3=49.50.51+50\)

\(S=0+1+1.2.3+2+2.3.4+3+...+49.50.51+50\)

\(=\left(1.2.3+2.3.4+...+49.50.51\right)+\left(1+2+...+50\right)\)

\(=\dfrac{49.50.51.52}{4}+\dfrac{50\left(50+1\right)}{2}=1625625\)

\(\Rightarrow A=2^3.1625625=13005000\)