Algebra
Binomial Theorem
In the expansion of \((2x+\frac{k}{x})^8\), where \(k\) is a positive constant, the term independent of \(x\) is \(700000\). Find \(k.\)
by
Noel Lo
\[\large \displaystyle \sum _{ r=0 }^{ n } { (-1 )}^{ r } { \binom{n}{r} }^{-1} \]
If \(n\) is an an odd positive integer, find the value of this sum.
by
shubham singh
\[ \left ( \sqrt {71} +1 \right )^{71} - \left ( \sqrt {71} -1 \right )^{71} \]
What is the last digit of the number above?
by
Joel Yip
What is the integral part of number \((\sqrt2+1)^6\)?
Details and Assumptions:
- As an explicit example, the integral part of \(123.456\) is \(123\).
by
Bhavya Jain
How many trailing zero(s) are there in the constant term of \( \left (x+\frac{1}{x} \right )^{2014}\)?
Details and Assumptions:
- The number of trailing zeroes in a number is the number of zeroes at the end of the number, e.g., \(100\) has \(2\) trailing zeroes, and \(100000001\) has none.
by
Nicolas Bryenton