Question

2倍的根号3减2倍的根号4分之1加上2分之3倍的根号4如何计算

2倍的根号1 +根号2 分之1 +3倍的根号2+2倍的根号3 分之1+4倍的根号3+3倍的根号4分之1•••+9倍的根号8+8倍的根号9

Answer 1

an=1/[(n+1)√n+n√(n+1)]
=[(n+1)√n-n√(n+1)]/[n(n+1)^2-(n+1)n^2]
=[(n+1)√n-n√(n+1)]/(n^3+2n^2+n-n^3-n^2)
=[(n+1)√n-n√(n+1)]/[n(n+1)]
=1/√n-1/√(n+1)
1/(2√1+√2)+1/(3√2+2√3)+...+1/(100√99+99√100)
=1-1/√2+1/√2-1/√3+1/√3-1/√4+...+1/√98-1/√99+1/√99-1/√100
=1-1/√100
=1-1/10
=9/10