The sum of the reciprocals of the first 11 terms in the harmonic progression series is 110. Determine the 6 terms of the harmonic progression series.

Reciprocals of first 11 terms will be AP

Therefore, S_n =  $\frac{n}{2}$ [2a + (n − 1) d]

S₁₁=110

n =11

110 =   $\frac{11}{2}\times$[2a + (11 − 1) d]

110 = $\frac{11}{2}\times$ [2a + 10d]

220 = 22a + 110d

22a + 110d = 220

a + 5d = 10

which is the 6^th term of the AP series

Therefore, the 6^th term in HP = $\frac{1}{10}$

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