1. Tardigrade
  2. Question
  3. Mathematics
  4. Let displaystyle∑ r =0100 displaystyle∑ s =0100( C r 2+ C s 2+ C r C s )= m ( 2 n C n )+2 p where m , n and p are even natural numbers and Cr represents the coefficient of xr in the expansion of (1+x)100. Find the value of (m+n+p).

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Q. Let $\displaystyle\sum_{ r =0}^{100} \displaystyle\sum_{ s =0}^{100}\left( C _{ r }^2+ C _{ s }^2+ C _{ r } C _{ s }\right)= m \left({ }^{2 n } C _{ n }\right)+2^{ p }$ where $m , n$ and $p$ are even natural numbers and $C_r$ represents the coefficient of $x^r$ in the expansion of $(1+x)^{100}$. Find the value of $(m+n+p)$.

Binomial Theorem

Solution:

Correct answer is '502'