一道数列放缩证明题,望大家不吝赐教!bn=1/(4n^2) .求证：当n≥1时,b1+(√2）b2+(√3)b3+.+(√n)bn

(√n)bn = (√n)/(4n^2) = (1/4) * n^(-3/2)b1+(√2）b2+(√3)b3+.+(√n)bn= (1/4) * (1^(-2/3) + 2^(-2/3) + 3^(-2/3) + ...+ n^(-2/3))估算 n^(-2/3) 的上界因为 1/√k - 1/√(k+1)= (√(k+1)-√k) / (√k√(k+1))...