Bài toán $15$ :
`\text{a . S = 1 - 2 + 3 - 4 + ... + 2005 - 2006}`
`\text{ S = ( 1 - 2 ) + ( 3 - 4 ) + ... + ( 2005 - 2006 )}`
`\text{ S = ( -1 ) + -1 + ... + -1}` ( $1003$ lần $-1$ )
`\text{ S = -1 × 1003 = -1003}`
`\text{b . S = 1 - 3 + 5 - 7 + ... + 2001 - 2003}`
`\text{ S = ( 1 - 3 ) + ( 5 - 7 ) + ... + ( 2001 - 2003 )}`
`\text{ S = ( -2 ) + -2 + ... + -2}` ( $1002$ lần số $-2$ )`
`\text{ S = -2 × 1002}`
`\text{ S = -2004}`
`\text{c . S = 2 - 4 + 6 - 8 + ... + 2008 - 2010}`
`\text{ S = ( 2 - 4 ) + ( 6 - 8 ) + ... + ( 2008 - 2010 )`
`\text{ S = ( -2 ) +-2 + ... + -2}` ( $1005$ lần số $-2$ )
`\text{ S = -2 × 1005}`
`\text{ S = -2010}`
Bài toán $16$ :
`(x+1)+(x+2)+(x+3)+...+(x+1000)=5750`
`=>` Có $1000$ ngoặc
`<=>1000x+(1+2+3+...+1000)`
`<=>1000x+[(1+1000)×1000]:2=5750`
`<=>1000x+(1001000:2)=5750`
`<=>1000x+200500=5750`
`<=>1000x=5750-200500`
`<=>1000x=-494750`
Vậy `x=-494750:1000=-494,75`
