(10 pts). Show that the within-cluster variation (WCV) satisfies k=1 C(i)=k,C(j)-k equals to Σ Σ 1x,-제12, where X,-1 Σα i) =k Xi ん
find sum
995 (-1)* Σ C, 1991 – k k k = 0 1991 - k
show by mathematical induction
Σ) Ε Σ k=1 k=1
evaluate
Σ(1) k=1 n (-1)* k+1 Σ(1). A=0
find the radius of convergence
2) Σ(*) k-kak 11 k=0. k=0 24 b) Σ d) Σ (1+ (*). Υ k=1 k=1
E3. Show that Σ(-1)k( ) = 0 for all positive integers n and k with 0-k-n E4. Show that (t) = Σ ( . 71 に0 k+1 k"d) for all positive integers n and k with 0 ksn
b) Using the binomial theorem show that Σ (-1)"/2 (n) cos" k(z) sink(z), Σ (-1)(k-1)/2C) cox"-"(x) sink(z). cos(nx) = sin(nx) = COS k-odd 6 marks]
-Σ rinkin + ml. Sequence c[n] is defined as c[n] x(n] = { 1,-1, 1 } as x[k] and 5-point DFT of c[n] as c[k]. (i) Calculate C[1]? 「[I] = 1-e^(-%72%pi/5)+6 alculate the 4-point DFT of sequence Your last answer was interpreted as follows: I-e + e- Incorrect answer. ii) Calculate i [] is the conjugate operator) -96 Your last answer was interpreted as follows:-i Incorrect answer.
-Σ rinkin + ml. Sequence c[n] is defined as c[n] x(n] = {...
Use
the Binomial Theorem to show that
Σ(-1): c(n, k)= 0 -0
p-1 mod 4, prove that Σ k ( )-0. Let p be an odd prıme. Suppose that p k=1
p-1 mod 4, prove that Σ k ( )-0. Let p be an odd prıme. Suppose that p k=1