Derive the formula of sum of terms of HP
Answers
Answer:
A series of terms is known as a HP series when their reciprocals are in arithmetic progression. Example: 1/a, 1/(a+d), 1/(a+2d), and so on are in HP because a, a + d, a + 2d are in AP. The nth term of a HP series is Tn =1/ [a + (n -1) d].
Step-by-step explanation:
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Step-by-step explanation:
The nth term of the Harmonic Progression (H.P) = 1/ [a+(n-1)d]
Where
“a” is the first term of A.P
“d” is the common difference
“n” is the number of terms in A.P
The above formula can also be written as:
The nth term of H.P = 1/ (nth term of the corresponding A.P)
Geometric Progression
Arithmetic Progression for Class 10
Sum of N-terms
Sequence and Series
Harmonic Progression Sum
If 1/a, 1/a+d, 1/a+2d, …., 1/a+(n-1)d is given harmonic progression, the formula to find the sum of n terms in the harmonic progression is given by the formula:
Sum of n terms, Sn=1dln{2a+(2n−1)d2a−d}
Where,
“a” is the first term of A.P
“d” is the common difference of A.P
“ln” is the natural logarithm