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8. Sequences and Series
hard
જો અનંત સમગુણોત્તર શ્રેણીનું પ્રથમ પદ $x$ અને તેનો સરવાળો $5$ હોય, તો = …….
A
$x > 10$
B
$10 < x < 0$
C
$0 < x < 10$
D
$x < -10$
Solution
$\frac{x}{{1\,\, – \,\,r}}\,\, = \,\,5\,$
$ \Rightarrow \,\,5\,\, – \,\,5r\,\, = \,\,x\,\, \Rightarrow \,\,r\,\, = \,\,1\,\, – \,\,\frac{x}{5}$
$|r|\,\, < \,\,1\,$ મુજબ એટલે કે $\left| {{\text{1}}\,\,{\text{ – }}\,\,\frac{x}{5}} \right|\,\, < \,\,1\,\,;\,$
$ – \,\,1\,\, < \,\,1\,\, – \,\,\frac{x}{5}\,\, < \,\,1$
$ – 5\,\, < \,\,5\, – \,x\,\, < \,\,5\,\, $
$ \,\, – \,10\,\, < \,\, – x\,\, < \,\,0\,\, $
$ \,\,10\,\, > \,\,x\,\, > \,\,0$
એટલે કે ${\text{0}}\,\, < \,\,{\text{x}}\, < \,\,{\text{10}}$
Standard 11
Mathematics
