Question

Fie suma 1/44+1/45+...+1/103 .
a) Câţi termeni are suma S ?
b) Arătaţi că S < 3/2.

Answer 1

a. 1=1;
⇒103-44+1=59+1=60⇒suma are 60 de termeni;
b. 3/2=1,5;
⇒1/44⇒cel mai mare termen;
⇒1/103⇒cel mai mic termen;
⇒1/44=0,0[27];
⇒1/103=0,0097;
⇒1/44+1/103=0,119[72]⇒0,119[72]<1,5⇒S<1,5;