If the second term of the expansion `[a^(1/(13))+a/(sqrt(a^(-1)))]^n`
is `14 a^(5//2)`
, then the value of `(^n C_3)/(^n C_2)`
is.
Text Solution
Verified by Experts
The correct Answer is:
B
a. We know that `.^(m)C_(r)+.^(m)C_(r-1)xx.^(n)C_(1)+.^(m)C_(r-2)xx.^(n)C_(2)+"….."+.^(n)C_(r)= .^(m+n)C_(r)` So, if `m, n gt r` and `m + n lt r`, then `.^(m)C_(r)+.^(m)C_(r-1)xx.^(n)C_(1)+.^(m)C_(r-2)xx.^(n)C_(2)+"….."+.^(n)C_(r)=0` b. if `m, n gt r` then `.^(m)C_(r)+.^(m)C_(r-1)xx.^(n)C_(1)+.^(m)C_(r-2)xx.^(n)C_(2)+"....."+.^(n)C_(r)=.^(m+n)C_(r)` c. If `m, n lt r lt m + n` then `.^(m)C_(m) x .^(n)C_(r-m) + .^(m)C_(m-1)xx.^(n)C_(r-m+1)` `+ .^(m)C_(m-2)xx.^(n)C_(r-m+2)+"...."+.^(m)C_(r-n)xx.^(n)C_(n)=.^(m+n)C_(r)` d. if `m lt r lt n` `.^(m)C_(m) xx .^(n)C_(r-m)+.^(m)C_(m-1)xx.^(n)C_(r-m+1) +.^(m)C_(m-2)xx.^(n)C_(r-m+2)+"....."+.^(n)C_(r)=.^(m+n)C_(r)`.
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