Đáp án+ Giải thích các bước giải:
a,
Đặt A = 100 2 − 99 2 + 98 2 − 97 2 + 96 2 − 95 2 + ... + 2 2 − 1 2
A = (100 2 − 99 2 ) + (98 2 − 97 2 ) + ... + (2 − 1 2 2 ) A = 2.100 − 1 + 2.98 − 1 + 2.96 − 1 + ... + 2.2 − 1 A = 2.(100 + 98 + ... + 2) − 50 A = − 2 2. [(100 − 2) : 2 + 1] .(100 + 2) 50 Các A = 50.102 − 50 A = 50.(201 − 1) A = 50.101 A = 5050
b,
3(22+1)(24+1).....(264+1)3(22+1)(24+1).....(264+1)
=(22−1)(22+1)(24+1)....(264+1)=(22−1)(22+1)(24+1)....(264+1)
=(24−1)(24+1).....(264+1)=(24−1)(24+1).....(264+1)
=(28−1)......(264+1)=2128−1
