Question

ma puteti ajuta sa rezolv exercitiile
1+2+2 la puterea a doua+2 la puterea a treia+,,,,,,,+2 la puterea osuta
2 ori (1+3+3 la puterea a doua +,,,,,,,,+ 2 la puterea patruzecfi si noua)
1+2+3+,,,,,+50-25 ori 50
3+6+9+,,,,,,,,+75-75

Answer 1

I.
S1 = 1+2+2² +2³ + ...........+2^102  (1)   2S1 = 2+2² + 2³ +............2^103    (2) (2) -(1)   ⇒ 2S1-S1 = S1 =( 2^103 - 1)

II. S2 = 1+3 +3² +..................+3^49                                                        3S2 =3+3²+3³ +.............3^50       3S2-S2 = 2S2 = 3^50 - 1                    S2 = (3^50 - 1)/2

III. 1+2+3+ .........+50 = 50×51/2 = 1275   1275 - 1250 = 25

IV.  3(1+2+3 +.........+24) = 3×24×25/2 = 900