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ISI2015-DCG-21
0
votes
95
views
The value of the term independent of $x$ in the expansion of $(1-x)^2(x+\frac{1}{x})^7$ is
$-70$
$70$
$35$
None of these
isi2015-dcg
combinatory
binomial-theorem
asked
Sep 18, 2019
in
Combinatory
gatecse
recategorized
Nov 14, 2019
by
Lakshman Patel RJIT
95
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$(x+a)^{n}$=$\sum \binom{n}{r} x^{n-r} a^{r}$ put x power zero find r then put r in equations
Ans=-70
answered
Sep 21, 2019
amit166
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Let $(1+x)^n = C_0+C_1x+C_2x^2+ \ldots +C_nx^n, \: n$ being a positive integer. The value of $\left( 1+\frac{C_0}{C_1} \right) \left( 1+\frac{C_1}{C_2} \right) \cdots \left( 1+\frac{C_{n-1}}{C_n} \right)$ is $\left( \frac{n+1}{n+2} \right) ^n$ $ \frac{n^n}{n!} $ $\left( \frac{n}{n+1} \right) ^n$ $\frac{(n+1)^n}{n!}$
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