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7.Binomial Theorem
medium
$\frac{{{C_0}}}{1} + \frac{{{C_1}}}{2} + \frac{{{C_2}}}{3} + .... + \frac{{{C_n}}}{{n + 1}} = $
A
$\frac{{{2^n}}}{{n + 1}}$
B
$\frac{{{2^n} - 1}}{{n + 1}}$
C
$\frac{{{2^{n + 1}} - 1}}{{n + 1}}$
D
એકપણ નહિ.
Solution
(c) Proceeding as above and putting $n+1=N$
So given term can be written as $\frac{1}{N}\left\{ {{\,^N}{C_1} + {\,^N}{C_2} + {\,^N}{C_3} + ….} \right\}$
= $\frac{1}{N}\left\{ {{2^N} – 1} \right\} = \frac{1}{{n + 1}}({2^{n + 1}} – 1)$
Standard 11
Mathematics
