Question

Tìm hiệu a – b biết :

a = 1 . 2 +2 . 3 + 3 .4 +……+ 98 . 99

b = 1²+2²+3²+…….+98²

^{HELP ME! PLEASE}

Answer 1

Ta có A =1.2 + 2.3 + 3.4 + ...+ 98.99
B = 1^2 + 2^2 + 3^2 +...+98^2 = 1.1+2.2+3.3+...+98.98
Suy ra: A-B= (1.2 + 2.3 + 3.4 + ...+ 98.99) - (1.1+2.2+3.3+...+98.98)
= (1.2-1.1) + (2.3-2.2) + (3.4-3.3) +...+ (98.99-98.98)
= 1(2-1) + 2(3-2) + 3(4-3) +...+ 98(99-98)
= 1.1 + 2.1 + 3.1 +...+ 98.1
= 1+ 2+ 3+...+ 98 = [98.(98+1)]/2= 98.99/2 = 4851

Chúc bạn học tốt!

Answer 2

a-b =\(\sum\left(n\left(n+1\right)-n^2\right)=\sum n\) với n =98

= 1+2+3+...+98 =49.99=4851