द्विपद प्रमेय का उपयोग कर `9^(5)` का मान ज्ञात कीजिए ।

Options

A. `59049`
B. `59048`
C. `59059`
D. `58049`

Answer

A

Explanation

`9^(5) = (10 - 1)^(5) = 10^(5) (1 - (1)/(10))^(9)`
`=10^(5)[1-.^(5)C_(1).(1)/(10)+.^(5)C_(2)((1)/(10))^(2)-.^(5)C_(3)((1)/(10))^(3)+.^(5)C_(4)((1)/(10))^(4)-.^(5)C_(5)((1)/(10))^(5)]`
`= 10^(5)[1-5.(1)/(10)+10.(1)/(10^(2))-10(1)/(10^(3))+5.(1)/(10^(4))-1.(1)/(10^(5))]`
`10^(5)-5.10^(4)+10.10^(3)-10.10^(2)+5.10-1`
`= 100000 - 5 xx 10000 + 10 xx 1000 - 10 xx 100 + 5 xx 10 - 1`
`= 100000 - 50000 + 10000 - 1000 + 50 - 1`
`= 110050 - 51001 = 59049`.