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The value of $\sum_{n=2}^{1947}\frac{1}{2^n+\sqrt{2^{1947}}}$ is equal to
A
$\frac{487}{\sqrt{2^{1945}}}$
B
$\frac{1946}{\sqrt{2^{1947}}}$
C
$\frac{1947}{\sqrt{2^{1947}}}$
D
$\frac{1948}{\sqrt{2^{1947}}}$
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The value of $\sum_{n=2}^{1947}\frac{1}{2^n+\sqrt{2^{1947}}}$ is equal to
Mathematics
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MediumSingle Correct
If $\binom{30}{1}^{2}+2\binom{30}{2}^{2}+3\binom{30}{3}^{2}+...+30\binom{30}{30}^{2}=\frac{\alpha(60!)}{(30!)^{2}}$ then $\alpha$ is equal to
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