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The value of 1- \(\frac{1}{20}+\frac1{20^2}-\frac1{20^3}\)+ ......... correct to 5 places of decimal is

(a) 1.05 

(b) 0.95238 

(c) 0.95239 

(d) 10.5

1 Answer

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Best answer

(b) 0.95238

Given exp. 
 = 1 - \(\frac{1}{20}+\frac1{20^2}-\frac1{20^3}\) + ............

= 1 - \(\frac{1}{20}+\frac1{400}-\frac1{8000}\) + ...........

= 1 – 0.05 + 0.0025 – 0.000125 +....... 

= 1.0025 – 0.050125 = 0.952375 = 0.95238.

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