Question

tìm x biết :

a, (x+1) + (x+3) +................+ (x+99)=0

b, 1 mũ 3 + 2 mũ 3 +3 mũ 3 +.....................+ 11 mũ 3=(x-1) mũ 2

Answer 1

\(\text{a) ( x + 1 ) + ( x + 3 ) + ..... + ( x + 99 ) = 0}\)

\(\Rightarrow\left(x+x+x+.....+x\right)+\left(1+3+5+....+99\right)=0\)

\(\text{Ta có :}\)

\(1+3+5+...+99=\frac{\left(99-1\right):2+1.\left(99+1\right)}{2}=2500\)

\(\Rightarrow50x+2500=0\)

\(\Rightarrow50x=-2500\)

\(\Rightarrow x=-50\)