TS EAMCET · Maths · Mathematical Induction
For \(n \in N\), the largest positive integer that divides \(81 n+20 n-1\) is \(k\). If \(S\) is the sum of all positive divisors of \(k\) then \(S-k=\)
- A 117
- B 130
- C 115
- D 127
Answer & Solution
Correct Answer
(A) 117
Step-by-step Solution
Detailed explanation
\(81^n+20 n-1 \Rightarrow(1+80)^n+20 n-1\) \(\begin{aligned} & =1+80 n+{ }^n C_2 \times 80^2 \times 1+\ldots .+20 n-1 \\ & =100 n+100 \times 8^2 \times{ }^n C_2+{ }^n C_3 80^3 \ldots \\ & =100\left(n+{ }^n C_2 \times 64 \ldots .\right) \\ & k=100=2^2 \times 5^2 \end{aligned}\)…
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