If A_k= [ array cc k-1 & k k-2 & k+1 array ] , then what is det (A₁ )+ det (A₂ )+ det (A₃ )+ + det (A₁₀₀ ) equal to?

Step-by-step solution

Since, A_K= [ array cc K-1 & K K-2 & K+1 array ] aligned |A_K | & =( K -1)( K +1)- K ( ~K -2) & = K ^2-1- K ^2+2 ~K =2 ~K -1 aligned Now, | A ₁ |+ | A ₂ |+ | A ₃ |+ . .+ | A ₁₀₀ | aligned & =(2 1-1)+(2 2-1)+(2 3-1)+ . & =1+(2 100-1) & =1+3+5+ .+199 & = 100 2 (1+199)=100 100=10000 aligned