Question

Solve for $2\left(1-\frac{1}{2}\right)+3\left(1-\frac{1}{3}\right)+4\left(1-\frac{1}{4}\right)+\ldots

+10\left(1-\frac{1}{10}\right)=?$
Hall please

Answer 1

`$2\left(1-(1)/(2)\right)+3\left(1-(1)/(3)\right)+4\left(1-(1)/(4)\right)+\ldots+10\left(1-(1)/(10)\right)=?$`

`2((2)/(2) -(1)/(2) )+3((3)/(3) -(1)/(3) )+4((4)/(4) -(1)/(4) )+5((5)/(5) -(1)/(5) )+6((6)/(6)-(1)/(6) )+7((7)/(7)-(1)/(7) )+8((8)/(8) -(1)/(8) )+9((9)/(9) -(1)/(9) )+10((10)/(10) -(1)/(10) )\\\\=2((1)/(2)) +3((2)/(3))+4((3)/(4))+5((4)/(5)) +6((5)/(6)) +7((6)/(7)) +8((7)/(8)) +9((8)/(9)) +10((9)/(10))\\\\=1+2+3+4+5+6+7+8+9\\\\=45`