Question

Tính

A=1*2+2*3+3*4+4*5+...+99*100

B=7*8*9+8*9*10+9*10*11+...+2015*2016*2017

C=1+3+3^2+3^3+3^4+3^5+...+3^49+3^50

Answer 1

\(A=\frac{99.100.101}{3}=333300\)

\(B=\frac{2015.2016.2017.2018}{4}-\frac{6.7.8.9}{4}=4133639960604\)

\(C=\frac{3^{51}-1}{3}+1\)

Answer 2

3A= 1.2.3+2.3.(4-1)+3.4.(5-2)+4.5.(6-3)+...+99.100.(101-98)

3A= 1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+4.5.6-3.4.5+...+99.100.101-98.99.100

3a= 99.100.101