What is the value of the following series1/7 + 2/72 + 1/73 +2/74 + 1/75 + ……….

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Nathan Mirro

  • Jul 26th, 2005
 

Following the pattern, the 1's and 2's repeat, and the other numbers increase... 

2/74 + 1/75 + 2/76 + 1/77 + 2/78 + 1/79, etc.

suman

  • Nov 13th, 2006
 

3/16 is the answer

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Sana

  • Aug 31st, 2007
 

1/7+1*[73^(-1) +.........................+(70+(2n+1))^-1+.......................]+2*[ 72^-1 + ........+(70+(2n))^-1+.................]


In the above series,the second term follows H.P with d=2 and a=73...reduce it using the sum of infinite terms in H.P----------------------------(1)

The third term also follows H.P with a= 72 and d=2..reduce it to the sum of infinite terms in H.P---------------------------(2)


use formula-> to simplify (1)  &  (2)

Now,add up (1),(2) and 1/7.

The above result will be the absolute answer!

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karthisiva

  • Dec 22nd, 2010
 

From the given equation the numbers are sequently incresed by one and decrease by 1 in numerator and in denominator it sequentialy increase by 1.

eg: 2/72+1/73+2/74

eg72,73,74,75.

so the next number is 76

and in numntr it incrs by 1

therefore the answer is 2/76+1/77+2/78...

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