find the sum of √3/2 , √2/3, 2/3,√2/3 ------------------- infinite terms
Answers
Answer:
Step-by-step explanation:
A series in which each term is formed by multiplying the corresponding terms of an A.P. and G.P. is called Arithmetico Geometric series. It is more popularly known as an A.G.P.
The general or standard form of such a series is a, (a +d) r, (a +2 d) r2 and so on.
Sum of infinite number of terms of an A.G.P with |r| < 1 is
S∞ =
Where,
a = first term
d = common difference of A.P.
r = common ratio of G.P.
The sum of first n natural numbers
= ∑ n = 1+ 2 + 3 + 4 +....+ n =
The sum of squares of first n natural numbers
= ∑ n2 = 12 + 22 + 32 +....+ n2 =
The sum of cubes of the first n natural numbers
= ∑ n3 = 1ˆ3 + 2ˆ3 + 3ˆ3 + 4ˆ3 +……+ nˆ3 =
Sum of first n odd natural numbers = 1+ 3 + 5 +......+ up to n terms = nˆ2.
Sum of first n even natural numbers = 2 +4 + 6 +......+ up to n terms = n (n+1).
For any series Tn = Sn – Sn-1
Fibonacci Series-In Fibonacci series, each term is the sum of previous two terms i.e.
F (n+1) = Fn + F (n-1) where n, n+1 and n-1 represent the term number).
Example: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233.....
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