Question

Calculati:
1pe1ori2+1pe2ori3+1pe3ori4+.....+1pe99ori100
Dau stea sau funda sau coroana si puncte

Answer 1

S=1^1+1^2+1^3+...+1^99|•1^1
S1=1^2+1^3+1^4+...+1^100
S1-S=1^2+1^3+1^4+...+1^100-1^1-1^2-1^3-...-1^99
S=1^100-1^1
S=1-1=0
0•2•3•4•...•99=0

Answer 2

1/(1x2) + 1/(2x3) + 1/(3x4) +.....+1/(99x100)
=(1/1-1/2) + (1/2-1/3) + (1/3-1/4) + .....+(1/99-1/100)
(aducand la acelasi numitor in fiecare paranteza, obtinem termenii initiali)
observam ca se reduc toti termenii in afara de primul si ultimul
deci rezultatul = 1/1-1/100, amlificam si=>99/100
R:99/100