Question

1. 10 + 21 + 32 + 43 + 54 + 65 + 76 + ... up to n terms.
2. 10 + 11 + 9 + 12 + 8 + 13 + 7 + ... up to n terms.
3. 1 + 2 + 3 - 5 + 6 + 7 - 9 + 10 + 11 ... up to n terms.
4. 1/2 + 2/3 + 3/4 + 4/5 + 5/6 + ... up to n terms.
5. 26 - 16 + 36 - 26 + 46 - 36 + 56 ... up to n terms.

Answer 1

import java.util.*;
class clSeries
{
    int fnSeries_1(int n)
    {
        int term = 10, sum = 0;
        for(int k = 1; k <= n; k++)
        {
            if(k == n)
            {
                System.out.print(term + " = ");
            }
            else
            {
                System.out.print(term + " + ");
            }
            sum = sum + term;
            term = term + 11;
        }
        System.out.println(sum);
        return sum;
    }
    void fnSeries_2A(int n)
    {
        int term = 0, ta = 10, tb = 11, sum = 0;
        String symbol = "+";
        System.out.print(" ");
        for(int k = 1; k <= n; k++)
        {
            if(k % 2 != 0)
            {
                term = ta;
                ta--;
            }
            else
            {
                term = tb;
                tb++;
            }
            sum = sum + term;
            symbol = (k == n) ? " = " : " + ";
            System.out.print(term + symbol);
        }
        System.out.println(sum);
    }
    //another method
    void fnSeries_2B(int n)
    {
        int term = 10, inc = 0, sum = 0, sign = 1;
        String symbol = "+";
        for(int k = 1; k <= n; k++)
        {
            sum = sum + term;
            symbol = (k == n) ? " = " : " + ";
            System.out.print(term + symbol);
            inc++;
            term = term + inc * sign;
            sign = sign * (-1);
        }
        System.out.println(sum);
    }
    void fnSeries_3(int n)
    {
        int term = 1, k = 1, sum = 0;
        String symbol = "+";
        while(k <= n)
        {
            if(term % 4 == 0)
            {
                term++;
            }
            sum = sum + term;
            symbol = (k == n) ? " = " : " + ";
            System.out.print(term + symbol);
            term++;
            k++;
        }
        System.out.println(sum);
    }
    void fnSeries_4(int n)
    {
        double f = 0, sum = 0;
        String symbol = " + ";
        for(int t = 1; t <= n; t++)
        {
            f = (double)t / (t + 1);
            sum = sum + f;
            symbol = (t == n) ? " = " : " + ";
            System.out.print(t + "/" + (t + 1) + symbol);
        }
        System.out.println(sum);
    }
    void fnSeries_5(int n)
    {
        int term = 26, inc = 0, sum = 0;
        String symbol = " - ";
        for(int k = 1; k <= n; k++)
        {
            sum = (k % 2 != 0) ? (sum + term) : (sum - term);
            inc = (k % 2 == 0) ? 20 : (-10);
            symbol = (k % 2 != 0) ? " - " : " + ";
            symbol = (k == n) ? " = " : symbol;            
            System.out.print(term + symbol);
            term = term + inc;
        }
        System.out.println(sum);
    }
    void main(String args[])
    {
        System.out.println("\nSERIES – I ");
        fnSeries_1(5);
        System.out.println("\nSERIES – II ");
        fnSeries_2A(5);
        System.out.println("\nSERIES – III ");
        fnSeries_3(5);
        System.out.println("\nSERIES – IV ");
        fnSeries_4(4);
        System.out.println("\nSERIES – V ");
        fnSeries_5(5);
        System.out.println("\n\nSERIES - II Again.. ");
        fnSeries_2B(7);
    }
}

Output:

SERIES-I
10 + 21 + 32 + 43 + 54 = 160 
SERIES-II
10 + 11 + 9 + 12 + 8 = 50 
SERIES - III
1 + 2 + 3 + 5 + 6 = 17 
SERIES - IV
1/2 + 2/3 + 3/4 + 4/5 = 2.7166999 
SERIES - V
26 - 16 + 36 - 26 + 46 = 66 
SERIES - II Again..
10 +11 + 9 + 12 + 8 + 13 + 7 = 70