Rahul's father wants to deposit some amounton his first birthday hundred rupees on his second birthday 300rupees on his third birthday600rupees on his 4th birthday 1000rupees and so onwhat is the Amount deposited by his father on Rahul's 15th Birthday
Answers
Answer:
Step-by-step explanation:
Multiples of 2: 2;4;...........100
Multiples of 5: 5;10..........100
In the above series some numbers are repeated twice these are multiples of 10 i.e LCM of 2 and 5
Sum of integers which are divisible by 2 and 5 from 1 to 100=
(Sum of integers which are divisible by 2 from 1 to 100) + (sum of integers which are divisible by 5 from 1 to 100) -(sum of integers which are divisible by 10 from 1 to 100) =
(2+4+......... +100) +(5+10+...... +100) -(10+20+...... 100)
=2(1+2+3+....... 50) + 5(1+2+3+.......20) -10(1+2+3+..... +10) =
2(50(50+1)) ÷2 + 5(20(20+1)) ÷2 -10(10(10+1)) ÷2
=(50(51)) +5(10(20+1) -5(10(11) =
50(51) +5(10(21)-5(10(11) =
2550+1050-550=
3600-550
=3050
Therefore sum of integers from 1 to 100 which are divisible by 2 or 5 is 3050