Question

[tung nguyen viet]

Giúp với

Tính tổng dãy số S=1*3+3*5+...+57*59

Answer 1

[Mr Lazy]

\(n\left(n+2\right)=\frac{1}{6}n\left(n+2\right)\left[\left(n+4\right)-\left(n-2\right)\right]=-\frac{1}{6}\left(n-2\right)n\left(n+2\right)+\frac{1}{6}n\left(n+2\right)\left(n+4\right)\)

\(\Rightarrow6S=-\left(-1\right).1.3+1.3.5-1.3.5+3.5.7-...-55.57.59+57.59.61\)

\(=3+57.59.61=205146\)