Question

Tính tổng

A=\(1^3+2^3+3^3+...+100^3\)

B=\(2^3+4^3+...+98^3\)

C=\(1^3+3^3+5^3+...+99^3\)

D=\(1^3-2^3+3^3-4^3+...+99^3-100^3\)

Answer 1

help me

Answer 2

a) Ta có: \(A=1^3+2^3+3^3+...+100^3\)

\(=\left(1-1\right)\cdot1\cdot\left(1+1\right)+1+\left(2-1\right)\cdot2\cdot\left(2+1\right)+2+...+\left(100-1\right)\cdot100\cdot\left(100+1\right)+100\)

\(=1+2+1\cdot2\cdot3+...+99\cdot100\cdot101\)

\(=5050+25497450\)

\(=25502500\)