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1!+ 2!+ 3!+ .... +95! is devided by 15. What is the remainder. How to solve?
opt: a.1. b13
c.14. d.3?
opt: a.1. b13
c.14. d.3?
Most Upvoted Answer
1!+ 2!+ 3!+ .... +95! is devided by 15. What is the remainder. How to ...
1!=1
2!=2 x 1 = 2
3!= 3 × 2 x 1 = 6
4!= 4 x 3 x 2 x 1 = 24
5!=5 x 4 x 3 x 2 x 1 (divisible by 15)
-. -
6!=6 x 5 x 4 x 3 x 2 x 1(divisible by 15)
-. -
here , 5! , 6! is divisible by 15
similarly next all full divisible by 15
let
s=1!+2!+3!+....+95!
dividing by 15 both sides
s/15 =( 1+2+6+24+15k)/15. , (let next number after the addition divided in k times by15)
now,
s/15 = 33/15. + 15k/15
again,
15)33(2
30
====
3
therefore remainder is 3
hence option d is correct
2!=2 x 1 = 2
3!= 3 × 2 x 1 = 6
4!= 4 x 3 x 2 x 1 = 24
5!=5 x 4 x 3 x 2 x 1 (divisible by 15)
-. -
6!=6 x 5 x 4 x 3 x 2 x 1(divisible by 15)
-. -
here , 5! , 6! is divisible by 15
similarly next all full divisible by 15
let
s=1!+2!+3!+....+95!
dividing by 15 both sides
s/15 =( 1+2+6+24+15k)/15. , (let next number after the addition divided in k times by15)
now,
s/15 = 33/15. + 15k/15
again,
15)33(2
30
====
3
therefore remainder is 3
hence option d is correct
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1!+ 2!+ 3!+ .... +95! is devided by 15. What is the remainder. How to solve?opt: a.1. b13 c.14. d.3?
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1!+ 2!+ 3!+ .... +95! is devided by 15. What is the remainder. How to solve?opt: a.1. b13 c.14. d.3? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 1!+ 2!+ 3!+ .... +95! is devided by 15. What is the remainder. How to solve?opt: a.1. b13 c.14. d.3? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 1!+ 2!+ 3!+ .... +95! is devided by 15. What is the remainder. How to solve?opt: a.1. b13 c.14. d.3?.
1!+ 2!+ 3!+ .... +95! is devided by 15. What is the remainder. How to solve?opt: a.1. b13 c.14. d.3? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 1!+ 2!+ 3!+ .... +95! is devided by 15. What is the remainder. How to solve?opt: a.1. b13 c.14. d.3? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 1!+ 2!+ 3!+ .... +95! is devided by 15. What is the remainder. How to solve?opt: a.1. b13 c.14. d.3?.
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