The sum of 7.7 , 7.07 , 7.007 and 77.0077is
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Answer:
Consider the given numbers 7+7.7+7.77+7.777+… to 50 terms
Take out 7 as common we get,
=7(1+1.1+1.11+1.111+….50 terms )
=7/9(9+9.9+9.99+9.999+….50 terms )
=7/9((10−1)+(10−0.1)+(10−0.01)+(10−0.001)+…50 terms )
=7/9(10+10+10+10+…n terms −(0.1+0.01+0.001+….50 terms ))
We know that, S
n
=a(1−r
n
)/(1−r)
=7/9[500−(1(1−(0.1)
50
)/(1−0.1))]
=7/9[500−((10/9)(1−(1/10
50
)))]
=7/81[4500−10+10
−49
]
=7/81[4490+10
−49
]
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