Question

Va rog muult..macar cateva,dau coroana!

a) 1/150+2/150+3/150+...+149/150=?
b) 17/42+18/42+19/42+...+84/42=?
c)1/50+2/50+3/50+...+51/50=?
d)1/50+2/50+3/50-4/50+...+99/50-100/50=?
e)1/225-2/225+3/225-4/225+...+449/225-450/225=?
f)1/99+2/99+3/99+...+199/99+200/99-201/99
g)1/3-$2/ 3^{2}$ -$2/ 3^{3}$ $-2/ 3^{4}$ - .... - $2/ 3^{30}$ =?

Answer 1

a) 1/150+2/150+3/150+...+149/150=1/150*(1+2+3...+149)=1/150*149*150/2=
=1/150*11175= 37/5


b) 17/42+18/42+19/42+...+84/42=1/42*(17+18+.....84)=1/42*101*68/2=
1/42*3434=3434/42=1717/ 17


c)1/50+2/50+3/50+...+51/50=?1/50*(1+2+3...+51)=1/50*52*51/2=1/50*1326
=26,52


d)1/50-2/50+3/50-4/50+...+99/50-100/50=1/50*(1-2+3-4+5-6+...+99-100)=
=1/50 *(-50)= -1


e)1/225-2/225+3/225-4/225+...+449/225-450/225=1/225*(-1-1-.....-1)=
1/225*(-225)=-1


f)1/99+2/99+3/99+...+199/99+200/99-201/99=1/99*(1+2+3+.....+200)-201/99= 1/99*200*201/2 -201/99=1/99*20100-201/99=19899/99=201