PATTERN-1
n=int(input("Enter the range of the pattern = "))
s=0
x=1
for i in range(1,n+1):
if i==n:
print(i,"!",end="",sep="")
elif i!=0:
print(i,"!",end="+",sep="")
for j in range (1,i+1):
x=x*j
s=s+x
x=1
print("\n","The sum of factorials =",s)
OUTPUT
Enter the range of the pattern = 5
1!+2!+3!+4!+5!
The sum of factorials = 153
PATTERN-2
n=int(input("Enter the range of the pattern = "))
s=0
x=1
for i in range(1,n+1):
if i==n:
print(i,"/",(i+1),end="",sep="")
elif i!=0:
print(i,"/",(i+1),end=" + ",sep="")
for j in range (1,i+1):
x=i/(j+1)
s=s+x
print("\n","The sum of the pattern =",s)
OUTPUT
Enter the range of the pattern = 5
1/2 + 2/3 + 3/4 + 4/5 + 5/6
The sum of the pattern = 3.5500000000000003
PATTERN-3
x=int(input("Enter the base of the pattern = "))
n=int(input("Enter the range of the pattern = "))
t=x
s=0
for i in range(1,n+1):
if i==n:
print(x,"^",i,end="",sep="")
else:
print(x,"^",i,end="+ ",sep="")
x=x**i
s+=x
x=t
print("\n","The sum of the number =",s)
OUTPUT
Enter the base of the pattern = 5
Enter the range of the pattern = 3
5^1+ 5^2+ 5^3
The sum of the number = 155
PATTERN-4
x=int(input("Enter the base of the pattern = "))
n=int(input("Enter the range of the pattern = "))
t=1
s=0
for i in range(1,n+1):
if i==n:
print(x,"^",i,"/",i,"!",sep="",end="")
else:
print(x,"^",i,"/",i,"!",sep="",end=" + ")
for j in range(1,i+1):
t=t*j
s+=(x**i)/t
t=1
print("\n","The sum of the numebers =",s)
OUTPUT
Enter the base of the pattern = 5
Enter the range of the pattern = 3
5^1/1! + 5^2/2! + 5^3/3!
The sum of the numbers = 38.33333333333333
PATTERN-5
n=int(input("Enter the range of the pattern = "))
x=0
s=0
print("1+(1+2)+(1+2+3)+(!+2+3+4)+.....(1+2+3+4+....+n)")
for i in range(1,n+1):
for j in range(1,i+1):
x=x+1
s+=x
print("\n","The sum of numbers =",s)
OUTPUT
Enter the range of the pattern = 3
1+(1+2)+(1+2+3)+(!+2+3+4)+.....(1+2+3+4+....+n)
The sum of numbers = 10
PATTERN-6
n=int(input("Enter the range of the pattern = "))
x=0
s=0
for i in range(0,n):
if i==n-1:
print(i+1,"^3",end="",sep="")
else:
print(i+1,"^3",end=" + ",sep="")
x=(i+1)**3
s+=x
x=0
print("\n","The sum of numbers =",s)
OUTPUT
Enter the range of the pattern = 5
1^3 + 2^3 + 3^3 + 4^3 + 5^3
The sum of numbers = 225