Toán Rút gọn bt 100 mũ 2-99 mũ 2+98 mũ 2+2 mũ 2 – 1mũ 2 06/09/2021 By Kennedy Rút gọn bt 100 mũ 2-99 mũ 2+98 mũ 2+2 mũ 2 – 1mũ 2
Đáp án: Giải thích các bước giải: Gọi tổng trên là S S=1002−992−982−....−1=1002−(100−1)2−(100−2)2−.....−(100−99)2=1002−1002−1002−.....−1002+2.100+2.2.100+2.3.100+.....+2.99.100−12−22−32−....−992−1002+1002S=1002−992−982−….−1=1002−(100−1)2−(100−2)2−…..−(100−99)2=1002−1002−1002−…..−1002+2.100+2.2.100+2.3.100+…..+2.99.100−12−22−32−….−992−1002+1002 A=12+22+992+1002A=12+22+992+1002 =1.(2-1)+2.(3-1)+3.(4-1)+….+99.(100-1)+100.(101-1) =1.2-1.1+2.3-1.2+3.4-1.3+…+99.100-1.99+100.101-1.100 =(1.2+2.3+3.4+…+99.100+100.101)-(1+2+3+…+100) = [1.2.3+2.3.(4-1)+3.4.(5-2)+…+100.101.(102-99) ] /3 + [(100+1).100 /2] =[1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+….+100.101.102-99.10.101]/3 + 5050 =100.101.102/3 + 5050 =348450 ⇒S=−99.1002+2.100.99.100−A=641550 Trả lời
Đáp án:
Giải thích các bước giải:
Gọi tổng trên là S
S=1002−992−982−....−1=1002−(100−1)2−(100−2)2−.....−(100−99)2=1002−1002−1002−.....−1002+2.100+2.2.100+2.3.100+.....+2.99.100−12−22−32−....−992−1002+1002S=1002−992−982−….−1=1002−(100−1)2−(100−2)2−…..−(100−99)2=1002−1002−1002−…..−1002+2.100+2.2.100+2.3.100+…..+2.99.100−12−22−32−….−992−1002+1002
A=12+22+992+1002A=12+22+992+1002
=1.(2-1)+2.(3-1)+3.(4-1)+….+99.(100-1)+100.(101-1)
=1.2-1.1+2.3-1.2+3.4-1.3+…+99.100-1.99+100.101-1.100
=(1.2+2.3+3.4+…+99.100+100.101)-(1+2+3+…+100)
= [1.2.3+2.3.(4-1)+3.4.(5-2)+…+100.101.(102-99) ] /3 + [(100+1).100 /2]
=[1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+….+100.101.102-99.10.101]/3 + 5050
=100.101.102/3 + 5050
=348450
⇒S=−99.1002+2.100.99.100−A=641550