Question

Arătați ca: a) 1/n(n+1)=1/n-1/n+1, n € N*;
b) k/n(n+k)=1/n-1/n+k, n,k € N*.
Folosind a) sau b), calculați următoarele sume:
S1=1/4•5+1/5•6+1/6•7+...+1/99•100;
S2=2/11•13+2/13•15+2/15•17+...+2/999•1001;
S3=1/23•25+1/25•27+1/27•29+...+1/1999•2001+1958/2001;
S4=2/n+4/n+6/n+...+2n-2/n., n € N* si n = 50;
S5=1/n•(n+1)+1/(n+1)(n+2)+1/(n+2)(n+3)+...+1/(n+10)(n+11), n € N*.

Answer 1

Ai ă si b in pozele atașate