4.1.3 Summation of Series

৪.১.৩ নিম্নোক্ত ধারা গুলোর যোগফল নির্ণয় কর।

1. [8] 1 + 2 + 3 + 4 + ......... + N

   1. [8.1] 1 + 2 + 3 + ......... + 100 (Similar)

2. [9] 1 + 3 + 5 + 7 + ......... + N

   1. [9.1] 1 + 3 + 5 + ......... + 30 (Similar)

   2. [9.2] ১ থেকে ৫০০ পর্যন্ত সব বিজোড় সংখ্যার যোগফল প্রিন্ট কর। (Similar)

   3. [9.3] 1 + 3 + 5 + ......... + 10 (Similar) [Used continue to skip even number]

   4. [9.4] 221+223+225+......+N (Similar)

3. [10] 2 + 4 + 6 + 8 + ......... + N

   1. [10.1] 2 + 4 + 6 + 8 + ......... + 100 (Similar)

4. [11] 1 + 4 + 7 + 10 + ......... + N

5. [12] 1 + 4 + 7 + 10 + ......... + N (উক্ত ধারার জোড় সংখ্যাগুলোর যোগফল নির্ণয় কর।)

6. [13] 1 + 4 + 7 + 10 + ......... + N (উক্ত ধারার বিজোড় সংখ্যাগুলোর যোগফল নির্ণয় কর।)

   1. 1 + 4 + 7 + 10 + ......... + 40 (Similar)

      1. [13.1] উক্ত ধারার জোড় সংখ্যাগুলোর যোগফল নির্ণয় কর।

      2. [13.2] উক্ত ধারার বিজোড় সংখ্যাগুলোর যোগফল নির্ণয় কর।

   2. [13.3] 1+5+9+.........+29 (Similar)

   3. [13.4] 3+7+11+.........+100 (Similar)

   4. [13.5] 3+6+9+……+n (Similar)

   5. [13.6] 5 + 10 + 15 + 20 + ......... + N (Similar)

      1. [13.7] 5 + 10 + 15 + ......... + 100 (Similar)

      2. [13.8] 20+25+30+......+50 (Similar)

   6. [13.9] 10 + 20 + 30 + ......... +n (Similar)

      1. [13.10] 10 + 20 + 30 + ......... + 100 (Similar)

   7. [13.11] 7+14+21+......+70 (Similar)

   8. [13.12] 10+16+22+......+70 (Similar)

7. [14] N + (N-1) + (N-2) + ......... + 4 + 3 + 2 + 1

   1. [14.1] N + (N-2) + (N-4) + ......... + 8 + 6 + 4 + 2 (Similar)

   2. [14.2] N + (N-2) + (N-4) + ......... + 7 + 5 + 3 + 1 (Similar)

   3. [14.3] N + (N-7) + (N-14) + (N-21) + ......... + 28 + 21 + 14 + 7 (Similar)

8. [15] 1^2 + 2^2 + 3^2 + 4^2 + ......... + N^2

   1. [15.1] 1^2 + 3^2 + 5^2 + 7^2 + ......... + N^2 (Similar)

   2. [15.2] 2^2+4^2+6^2+......+80^2 (Similar)

   3. [15.3] 2^2+5^2+8^2+11^2+......+n^2 (Similar)

   4. [15.4] 3^2 + 7^2 + 11^2 + ......... + n^2 (Similar)

   5. [15.5] 9^2+12^2+15^2+......+90^2 (Similar)

   6. [15.6] 3^2+6^2+9^2+……+n^2 (Similar)

9. [16] 2^3 + 4^3 + 6^3 + 8^3 + ......... + N^3

10. [17] N^2 + (N-10)^2 + (n-20)^2 + .........+ 40^2 + 30^2 + 20^2 + 10^2

    1. [17.1] 90^2+80^2+70^2+......+20^2 (Similar)

11. [18] 1×2 + 2×3 + 3×4 × ......... + N×(N+1)

সমাধান

[8] 1 + 2 + 3 + 4 + ......... + N

for 1

#include<stdio.h>
int main(){
    int n, i, sum;
    
    scanf("%d", &n);
    sum = 0;
    for(i = 1; i <= n; i++){
        sum = sum + i;
    }
    printf("%d\n", sum);

    return 0;
}

for 2

#include<stdio.h>
int main(){
    int n, i, sum;
    
    scanf("%d", &n);
    for(sum = 0, i = 1; i <= n; i++){
        sum = sum + i;
    }
    printf("%d\n", sum);

    return 0;
}

for 3

#include<stdio.h>
int main(){
    int n, i, sum = 0;
    
    scanf("%d", &n);
    for(i = 1; i <= n; i++){
        sum = sum + i;
    }
    printf("%d\n", sum);

    return 0;
}

for 4

#include<stdio.h>
int main(){
    int n, i, sum = 0;
    
    scanf("%d", &n);
    for(i = 1; i <= n; i++){
        sum += i;
    }
    printf("%d\n", sum);

    return 0;
}

while 1

#include<stdio.h>
int main(){
    int n, i = 1, sum = 0;
    
    scanf("%d", &n);
    while(i <= n){
        sum += i;
        i++;
    }
    printf("%d\n", sum);

    return 0;
}

while 2

#include<stdio.h>
int main(){
    int n, i = 1, sum = 0;
    
    scanf("%d", &n);
    while(i <= n){
        sum += i++;
    }
    printf("%d\n", sum);

    return 0;
}

do while

#include<stdio.h>
int main(){
    int n, i = 1, sum = 0;
    
    scanf("%d", &n);
    do{
        sum += i++;
    }while(i <= n);
    printf("%d\n", sum);

    return 0;
}

formula

#include<stdio.h>
int main(){
    int n, sum = 0;
    
    scanf("%d", &n);
    
    sum = n * (n + 1) / 2;
    
    printf("%d\n", sum);

    return 0;
}

Sample Input	Sample Output
10	55
100	5050

[9] 1 + 3 + 5 + 7 + ......... + N

#include<stdio.h>
int main(){
    int n, i, sum = 0;
    
    scanf("%d", &n);
    for(i = 1; i <= n; i += 2){
        sum += i;
    }
    printf("%d\n", sum);

    return 0;
}

Sample Input	Sample Output
10	25
100	2500

[10] 2 + 4 + 6 + 8 + ......... + N

#include<stdio.h>
int main(){
    int n, i, sum = 0;
    
    scanf("%d", &n);
    for(i = 2; i <= n; i += 2){
        sum += i;
    }
    printf("%d\n", sum);

    return 0;
}

Input	Sample Output
10	30
100	2550

[11] 1 + 4 + 7 + 10 + ......... + N

#include<stdio.h>
int main(){
    int n, i, sum = 0;
    
    scanf("%d", &n);
    for(i = 1; i <= n; i += 3){
        sum += i;
    }
    printf("%d\n", sum);

    return 0;
}

Sample Input	Sample Output
10	22
100	1717

[12] 1 + 4 + 7 + 10 + ......... + N (উক্ত ধারার জোড় সংখ্যাগুলোর যোগফল নির্ণয় কর।)

#include<stdio.h>
int main(){
    int n, i, sum = 0;
    
    scanf("%d", &n);
    for(i = 1; i <= n; i += 3){
        if( i % 2 == 0 ){
            sum += i;
        }
    }
    printf("%d\n", sum);

    return 0;
}

Sample Input	Sample Output
10	14
100	884

[13] 1 + 4 + 7 + 10 + ......... + N (উক্ত ধারার বিজোড় সংখ্যাগুলোর যোগফল নির্ণয় কর।)

#include<stdio.h>
int main(){
    int n, i, sum = 0;
    
    scanf("%d", &n);
    for(i = 1; i <= n; i += 3){
        if( i % 2 == 1 ){
            sum += i;
        }
    }
    printf("%d\n", sum);

    return 0;
}

Sample Input	Sample Output
10	8
100	833

[14] N + (N-1) + (N-2) + ......... + 4 + 3 + 2 + 1

#include<stdio.h>
int main(){
    int n, i, sum = 0;
    
    scanf("%d", &n);
    for(i = n; i >= 1; i--){
        sum += i;
    }
    printf("%d\n", sum);

    return 0;
}

Sample Input	Sample Output
10	55
100	5050

[15] 1^2 + 2^2 + 3^2 + 4^2 + ......... + N^2

loop

#include<stdio.h>
int main(){
    int n, i, sum = 0;
    
    scanf("%d", &n);
    for(i = 1; i <= n; i++){
        sum += i * i;
    }
    printf("%d\n", sum);

    return 0;
}

formula

#include <stdio.h>

int main() {
    int n, sum;
    
    scanf("%d", &n);
    sum = n * (n + 1) * (2 * n + 1) / 6;
    printf("%d\n", sum);

    return 0;
}

Sample Input	Sample Output
10	385
100	338350

[16] 2^3 + 4^3 + 6^3 + 8^3 + ......... + N^3

#include<stdio.h>
int main(){
    int n, i, sum = 0;
    
    scanf("%d", &n);
    for(i = 2; i <= n; i += 2){
        sum += i * i * i;
    }
    printf("%d\n", sum);

    return 0;
}

Sample Input	Sample Output
10	1800
20	24200

[17] N^2 + (N-10)^2 + (n-20)^2 + .........+ 40^2 + 30^2 + 20^2 + 10^2

#include<stdio.h>
int main(){
    int n, i, sum = 0;
    
    scanf("%d", &n);
    for(i = n; i >= 10; i -= 10){
        sum += i * i;
    }
    printf("%d\n", sum);

    return 0;
}

Sample Input	Sample Output
50	5500
90	28500

[18] 1×2 + 2×3 + 3×4 × ......... + N×(N+1)

#include<stdio.h>
int main(){
    int n, i, sum = 0;
    
    scanf("%d", &n);
    for(i = 1; i <= n; i++){
        sum += i * (i + 1);
    }
    printf("%d\n", sum);

    return 0;
}

Sample Input	Sample Output
5	70
10	440