KVPY 2014 problem

This problem was asked in KVPY 2014 held on 2nd November SA stream

The value of -

$\sum _{ n=0 }^{ 1947 }{ \frac { 1 }{ { 2 }^{ n }+\sqrt { { 2 }^{ 1947 } } } }$

is equal to-

A. $\frac { 487 }{ \sqrt { { 2 }^{ 1945 } } }$

B. $\frac { 1946 }{ \sqrt { { 2 }^{ 1947 } } }$

C. $\frac { 1947 }{ \sqrt { { 2 }^{ 1947 } } }$

D. $\frac { 1948 }{ \sqrt { { 2 }^{ 1947 } } }$

#Algebra #KVPY #Summation #Kvpy2014

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

@Karthik Sharma Combine the first and the last term, then the 2nd and 2nd last.. See what happens

Pratik Shastri - 6 years, 7 months ago

Oh! yes got it now. Its 'A'.

Karthik Sharma - 6 years, 7 months ago

how

rakesh kanna - 3 years, 7 months ago

DUDE APKO NI PTA

Navdeep Nainwal - 6 years, 7 months ago

As we devide same digits we get ans. 1 what happen in this 0/0.

sahil kumar - 6 years, 7 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$