Question

12. Calculați sumele: a) 1+2+3+...+ 150; b) 2 +4 +6+...+ 200; c) 1+3+5+...+ 101; d) 10+12 + 14 + ... + 420; e) 2+ 2² +2+...+230; f) 3+3² +3³ +...+35⁰ .​

Answer 1

Explicație pas cu pas:

a) 1+2+3+...+ 150;

b) 2 +4 +6+...+ 200

; c) 1+3+5+...+ 101

; d) 10+12 + 14 + ... + 420

; e) 2+ 2² +2+...+230

; f) 3+3² +3³ +...+35⁰ .

a=n(n+1)/2= 150(150+1)/2=150*151/2=75*151=11325

b=n(n+1)/2=200(200+2)/2=200*202/2=100*202=20200

c=n(n+1)/2=101(101+1)/2=101*102/2=101*51=5151

d= =420(420+10)/2=420*430/2=210*430=90300

e= =230(230+2)/2=230*232/2=115*232=49880

f= [a^(n+1)-1 ] /a-1=[3^(50+1)-1]/3-1=3^(51)-1/2=