द्विपद प्रमेय की सहायता से सिद्ध कीजिए कि- `101^(50)gt100^(50)+99^(50)`

Explanation

`(101)^(50)-(100^(50)+99^(50))`
`=101^(50)-100^(50)-99^(50)`
`=(100+1)^(50)-(100-1)^(50)-100^(50`
`=[100^(50)+.^(50)C_(1)*100^(49)+.^(50)C_(2)*100^(48) +...+.^(50)C_(49)*100+1]-[100^(50)-.^(50)C_(1)*100^(49)+.^(50)C_(2)*100^(48)+...-.^(50)C_(49)*100+1]-100^(50)`
`=100^(50)+2xx.^(50)C_(3)xx100^(47)+...+2xx.^(50)C_(49)xx100-100^(50)`
`=2xx.^(50)C_(3)xx100^(47)+...+2xx.^(50)C_(49)xx100gt0`
`therefore101^(50)-(100^(50)+99^(50))gt0`
`rArr101^(50)gt100^(50)+99^(50)` यही सिद्ध करना था।