"Let A = {n $\in$ N | n2 $\le$ n + 10,000}, B = {3k + 1 | k$\in$ N} an dC = {2k | k$\in$N}, then the sum of all the elements of the set A $\cap$(B $-$ C) is equal to _____________."

Question

Accepted Answer

"B $-$ C $\equiv$ {7, 13, 19, ......, 97, .......}

Now, n² $-$ n $\le$ 100 $\times$ 100

$\Rightarrow$ n(n $-$ 1) $\le$ 100 $\times$ 100

$\Rightarrow$ A = {1, 2, ......., 100}.

So, A$\cap$(B $-$ C) = {7, 13, 19, ......., 97}

Hence, sum = ${{16} \over 2}(7 + 97) = 832$"

Let A = {n $\in$ N | n² $\le$ n + 10,000}, B = {3k + 1 | k$\in$ N} an dC = {2k | k$\in$N}, then the sum of all the elements of the set A $\cap$(B $-$ C) is equal to _____________.

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Let A = {n $\in$ N | n2 $\le$ n + 10,000}, B = {3k + 1 | k$\in$ N} an dC = {2k | k$\in$N}, then the sum of all the elements of the set A $\cap$(B $-$ C) is equal to _____________.

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Let A = {n $\in$ N | n² $\le$ n + 10,000}, B = {3k + 1 | k$\in$ N} an dC = {2k | k$\in$N}, then the sum of all the elements of the set A $\cap$(B $-$ C) is equal to _____________.