Sum of Series

1)      S = 1 + 2 + 3 + 4 + 5

2)      S = 1 + 2 + 3 + 4 + 5 + . . . + n

3)      S = 1 + 3 + 5 + 7 + 9 + . . . + n

4)      S = 2 + 4 + 6 + 8 + 10 + . . . + n

5)      S = 12 + 22 + 32 + 42 + 52 + . . . + n2 

6)      S = 13 + 23 + 33 + 43 + 53 + . . . + n3 

7)      S = 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 +……+ 1/n

8)      S = 1/12 + 1/22 + 1/32 + 1/42 + 1/52 + . . . +1/ n2 

9)      S = 1 - 2 + 3 - 4 + 5 + . . .  n

10)   S = 1/1! + 2/2! + 3/3! + …… + n/n!  

  11) Write a Java Program to print Fibonacci Series.

[In Fibonacci Series, next number is the sum of previous two numbers for example 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 etc. The first two numbers of Fibonacci series are 0 and 1. ]

12) Write a Java Program to print Tribonacci Series.

[The Tribonacci series is similar to the Fibonacci series. The Tribonacci sequence is a generalization of the Fibonacci sequence where each term is the sum of the three preceding terms. example 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149]

13) Write a Java Program to print t the first 15 terms of the Pell Series. 

The Pell numbers are an infinite sequence of integers. The sequence of Pell numbers starts with 0 and 1, and then each Pell number is the sum of twice the previous Pell number and the previous number. The first few terms of the sequences are: 0, 1, 2, 5, 12, 29, 70,……. 70 = 2 x 29 + 12; Hence, 70 is a Pell number 

Other Pell Numbers are: 0 1 2 5 12 29 70 169 408 985 2378 5741 13860 33461 80782