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7.Binomial Theorem
normal
$\sum\limits_{n = 0}^4 {{{\left( {1009 - 2n} \right)}^4}\left( \begin{gathered}
4 \hfill \\
n \hfill \\
\end{gathered} \right)} {\left( { - 1} \right)^n}$ ની કિમત મેળવો
A
$512$
B
$272$
C
$384$
D
$264$
Solution
$\sum\limits_{n = 0}^4 {{{\left( {1009 – 2n} \right)}^4}} {\,^4}{C_n}{\left( { – 1} \right)^n}$
$(1009)^{4}-4(1007)^{2}+6 \cdot(1005)^{4}-4(1003)^{4}+(1001)^{4}$
$(1005+4)^{4}+(1005-4)^{4}$
$-4\left[(1005+2)^{4}+(1005-2)^{4}\right]+6(1005)^{4}$
$=512-4 \times 32=384$
Standard 11
Mathematics
