Question

cum se rezolva si etapele de rezolvare a ex 40 punctul b

Answer 1

1/(√2 +2√1) + 1/(2√3+ 3√2) +1/(3√4+4√3).......+ 1/[n√(n+1) +(n+1)√n] =
= (√2 - 2)/(-2) + (2√3 -3√2)/(-6) + (3√4 -4√3)/(- 12)+......+
+ [n√(n+1) - (n+1)√n] /[ n²(n+1) - n·(n+1)²=
= -√2/ 2 + 1 - √3 /3 + √2 /2 - √4/4 + √3 /3 +....+ [n√(n+1) - (n+1)√n]/[-n(n+1)] =
= 1 + √n /n