Question
If X = {8n−7n−1:n∈N} and Y={49(n−1):n∈N} , then
Answer: Option A
:
A
Since 8n−7n−1=(7+1)n−7n−1
= 7n+nC17n−1+nC27n−2+.....+nCn−17+nCn−7n−1
= nC272+nC373+...+nCn7n,(nC0=nCnnC1=nCn−1etc,)
= 49[nC2+nC3(7)+........+nCn7n−2]
∴ 8n−7n−1 is a multiple of 49 for n ≥ 2
For n = 1 , 8n−7n−1=8−7−1=0;
For n = 2, 8n−7n−1=64−14−1=49
∴ 8n−7n−1 is a multiple of 49 for n ≥ N
∴ X contains elements which are multiples of 49 and clearlyγ
contains all multiplies of 49. ∴ X ⊆ Y.
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:
A
Since 8n−7n−1=(7+1)n−7n−1
= 7n+nC17n−1+nC27n−2+.....+nCn−17+nCn−7n−1
= nC272+nC373+...+nCn7n,(nC0=nCnnC1=nCn−1etc,)
= 49[nC2+nC3(7)+........+nCn7n−2]
∴ 8n−7n−1 is a multiple of 49 for n ≥ 2
For n = 1 , 8n−7n−1=8−7−1=0;
For n = 2, 8n−7n−1=64−14−1=49
∴ 8n−7n−1 is a multiple of 49 for n ≥ N
∴ X contains elements which are multiples of 49 and clearlyγ
contains all multiplies of 49. ∴ X ⊆ Y.
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