Question

a,M=100²-99²+98²-97²+...+2²-1²

b, N=(20²+18²+16²+...+4²+2²)-(19²+17²+15²+...+3²+1²)

c,P=(-1)ⁿ.(-1)²ⁿ⁺¹.(-1)ⁿ⁺¹

^{các bạn giúp mình nhanh nha. Cảm ơn trước}

Answer 1

a) \(M=100^2-99^2+98^2-97^2+...+2^2-1^2\)

\(M=(100^-99^2)+(98^2-97^2)+...+(2^2-1^2)\)

\(=(100-99)(100+99)+(98-97)(98+97)+...+(2-1)(2+1)\)

\(=100+99+98+97+...+2+1\)

\(=\frac{100(100+1)}{2}=5050\)

b) \(N=(20^2-19^2)+(18^2-17^2)+...+(2^2-1^2)\)

\(=(20-19)(20+19)+(18-17)(18+17)+...+(2-1)(2+1)\)

\(=20+19+18+17+...+2+1=\frac{20(20+1)}{2}=210\)

c) \(P=(-1)^n(-1)^{2n+1}(-1)^{n+1}\)

\(P=(-1)^{n+2n+1+n+1}=(-1)^{4n+2}=(-1)^{2(2n+1)}=1\)