1. Sa se calculeze:
a)1*2*3*4+2*3*4*5+...+n*(n+1)*(n+2)*(n+3)

b)1^2/(1*3)+2^2/(3*5)+...+n^2/(2n-1)(2n+1)

c) 4*1/(4*1^4+1)+4*2/(4*2^4+1)+....4*n/(4*n^4+1)


Sa se arate ca:
a)1/(1*4) +1/(4*7)+...+1/(3n-2)(3n+1)<(n+1)/(3n+1)

b)1/(n+1)+1/(n+2)+...+1/(3n+1)>1

c)(1*2)^1/2+(3*4)^1/2+...+[(2n-1)*2n]^1/2< (2*n^2+n)/2

La 1a) arata mai intai ca :

apoi dai valori lui n, gasesti formula ptr suma si in final inductia...