If 7=5+1 7 (5+ )+1 7^ 2 (5+2 )+1 7^ 3 (5+3 )+ , then the value of… - Vidyadip

MCQ

If $7=5+\frac{1}{7}(5+\alpha)+\frac{1}{7^{2}}(5+2 \alpha)+\frac{1}{7^{3}}(5+3 \alpha)+$ $\infty$, then the value of $\alpha$ is:

A
1
B
$\frac{6}{7}$
✓
6
D
$\frac{1}{7}$

✓

Answer

Correct option: C.

6

(C)
Sol. Let $\mathrm{S}=5+\frac{1}{7}(5+\alpha)+\frac{1}{7^{2}}(5+2 \alpha)+\ldots$
$\frac{1}{7} \mathrm{~S}=\frac{1}{7}(5)+\frac{1}{7^{2}}(5+\alpha)+\ldots \infty$
$\frac{6}{7}(S)=5+\frac{1}{7} \alpha\left(\frac{1}{1-\frac{1}{7}}\right)$
$6=5+\frac{\alpha}{6} \Rightarrow \alpha=6$

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