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Sum the following series to n terms: 1/(...

Sum the following series to `n` terms: `1/(1. 6)+1/(6. 11)+1/(11. 16)+1/(16. 21)+........ `infinite terms

A

5

B

`1/5`

C

infinite

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
GIven,`1/(1. 6)+1/(6. 11)+1/(11. 16)+1/(16. 21)+........ `
=`[(6-1)/(5.1.6)+(11-6)/(5.11.6)+......+((5n+1)-(5n-4))/(5.(5n-4).(5n+1))]`
=`1/5[(6-1)/(1.6)+(11-6)/(6.11)+...+((5n+1)-(5n-4))/((5n-4).(5n+1))]`
=`1/5[1-1/6+1/6-1/11+....+1/(5n-4)-1/(5n+1)]`
=`1/5[1-1/(5n+1)]`
=`n/(5n+1)`
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