Example 15 - Chapter 8 Class 11 Binomial Theorem (Deleted)
Last updated at Jan. 29, 2020 by
Last updated at Jan. 29, 2020 by
Transcript
Example 15 Find the term independent of x in the expansion of (βπ₯ " + " 1/(2 βπ₯))^18, x > 0. Calculating general term of expansion We know that general term of (a + b)n is Tr+1 = nCr (a)nβr . (a)n For general term of expansion (βπ₯ " + " 1/(2 βπ₯))^18 Putting n = 18 , a = βπ₯ , b = 1/(2 βπ₯) β΄ Tr + 1 = 18Cr (βπ₯)18 β r (1/(2 βπ₯))^π = 18Cr (γπ₯")" γ^(1/3 Γ (18 β π)) (1/2 "Γ" 1/βπ₯)^π = 18Cr (γπ₯")" γ^((18 β π)/3 ) (1/2)^π (1/βπ₯)^π = 18Cr (γπ₯")" γ^((18 β π)/3 ) 1/2^π (1/π₯^(1/3) )^π = 18Cr (γπ₯")" γ^((18 β π)/3 ) 1/2^π 1/π₯^(π/3) = 18Cr (γπ₯")" γ^((18 β π)/3 ) 1/2^π π₯^((βπ)/3) = 18Cr (γπ₯")" γ^((18 β π)/3 ) π₯^((βπ)/3) 1/2^π = 18Cr (γπ₯")" γ^((18 β π)/3 β π/3) 1/2^π = 18Cr (γπ₯")" γ^((18 β π β π)/3 ) 1/2^π = 18Cr (γπ₯")" γ^((18 β 2π)/3 ) 1/2^π β΄ Tr + 1 = 18Cr (γπ₯")" γ^((18 β 2π)/3 ) 1/2^π We need to find the term independent of x So, power of x is 0 π₯^((18 β2π)/3) = x0 Comparing power (18 β 2π)/3 = 0 18 β 2r = 0 18 = 2r 18/2 = r 9 = r r = 9 Putting r = 9 in (1) Tr+1 = 18Cr (γπ₯")" γ^((18 β 2π)/3 ) 1/2^π T9+1 = 18C9 .π₯^((18 β3(9))/3). 1/29 = 18C9 .x0. 1/29 = 18C9 . 1/29 Hence, the term which is independent of x is 10th term = T10 = 18C9 . π/ππa
Examples
Example 2 Important Deleted for CBSE Board 2022 Exams
Example 3 Important Deleted for CBSE Board 2022 Exams
Example 4 Deleted for CBSE Board 2022 Exams
Example 5 Important Deleted for CBSE Board 2022 Exams
Example 6 Important Deleted for CBSE Board 2022 Exams
Example 7 Deleted for CBSE Board 2022 Exams
Example 8 Important Deleted for CBSE Board 2022 Exams
Example 9 Deleted for CBSE Board 2022 Exams
Example 10 Important Deleted for CBSE Board 2022 Exams
Example 11 Important Deleted for CBSE Board 2022 Exams
Example 12 Deleted for CBSE Board 2022 Exams
Example 13 Important Deleted for CBSE Board 2022 Exams
Example 14 Important Deleted for CBSE Board 2022 Exams
Example 15 Important Deleted for CBSE Board 2022 Exams You are here
Example 16 Deleted for CBSE Board 2022 Exams
Example 17 Important Deleted for CBSE Board 2022 Exams
Examples
About the Author