Question

(2√5+1)(1∕√2+√3+1/√3+√4+1/√4+√5+﹍+1/√99+√100)

Answer 1

(2√5+1)[1∕(√2+√3)+1/(√3+√4)+1/(√4+√5)+﹍+1/(√99+√100)]

=(2√5+1) {(√3-√2) ∕ [(√3+√2)(√3-√2)]+(√4-√3) ∕ [(√4+√3)(√4-√3)]+(√5-√4) ∕ [(√5+√4)(√5-√4)]+﹍+(√100-√99) ∕ [(√100+√99)(√100-√9)] }

=(2√5+1) [(√3-√2)+(√4-√3)+(√5-√4)+﹍+(√100-√99)}

＝(2√5+1) (√100-√2)

＝(2√5+1) (10-√2)

( ＝20√5－2√10+10－√2 )