formula for sum of special series The following are the three types of special series 1 2 3 n sum of first n natural numbers 1 2 2 2 3 2 n 2 sum of squares of the first n natural numbers 1 3 2 3 3 3 n 3 sum of cubes of the first n natural
This article will walk you through three commonly used special series and how to derive formulas to calculate the sum of these series up to n terms We ll also provide solved So for a finite geometric series we can use this formula to find the sum This formula can also be used to help find the sum of an infinite geometric series if the series converges Typically
formula for sum of special series
formula for sum of special series
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SEQUENCES SERIES CLASS 11 SUM OF SPECIAL SERIES EX 9 4 NCERT YouTube
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Class 11 Maths 2019 Q13 Sum To N Terms Of Special Series YouTube
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Series Formulas 1 Arithmetic and Geometric Series Definitions First term a 1 Nth term a n Number of terms in the series n Sum of the first n terms S n Difference between successive To find the sum of the first nnn terms of an arithmetic series you can use the formula S n n 2 2a n 1 d How do you calculate the sum of a geometric series A
Sum to n terms of Special Series Let s try to find the formula to find the sum of the above special series i S n 1 2 3 4 n Here we have to find the sum of the first n natural numbers This is an arithmetic progression as we can Special Series A series can be defined as the sum of all the numbers of the given sequence The sequences are finite as well as infinite In the same way the series can also
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Let s look at some of the examples of the special series 1 2 3 n 12 22 32 n2 13 23 33 n3 The first equation is the sum of the n natural numbers whereas the Step 1 Find the sum from 1 upto the last term we have in the given series Step 2 Find the sum from 1 upto the preceding term of the first term what we have in the given series Step 3 By
There are some series whose sum can be expressed by explicit formulae Such series are called special series 1 Sum of first n natural numbers 2 Sum of first n odd natural numbers 3 Sum of squares of first n natural numbers 4 Sum of The sum of the k th group S k where the first term is a k frac k 1 k 2 1 and the number of terms is k can be found using the formula for the sum of an AP S k
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formula for sum of special series - Sum to n terms of Special Series Let s try to find the formula to find the sum of the above special series i S n 1 2 3 4 n Here we have to find the sum of the first n natural numbers This is an arithmetic progression as we can