Write the remainder obtained when 1! + 2! + 3! + ... + 200! is di… - Vidyadip

Question

Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14.

✓

Answer

First we will find the least factorial term divisible by 14.
As 7!=7 × 6 × 5! is divisible by 14 leaving remainder zero.
Hence terms 7! onwards can be written as multiple of 7!.
8!=8 × 7!, 9! = 9 × 8 × 7!... like ways 200! can also be written as multiple of 7!.
So all the terms 7! onwards are divisible by 14 leaving remainder zero.
= 1! + 2! + 3! + 4! + 5! + 6!
= 1 + 2 + 6 + 24 + 120 + 720
= 873
Hence remainder obtained when 1! + 2! + 3! + ….+ 200! is divided by 14 is 5.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "1 Marks Question" from Permutations→Permutations — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

P(A)	P(B)	P(A$\cap$B)	P(A$\cup$B)
0.5	0.35	________	0.7

Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2,11)}. Is the following given statement true? f is a relation from A to B. Justify your answer.

Prove that:
$2\cos\frac{5\pi}{12}\cos\frac{\pi}{12}=\frac{1}{2}$

If the minor axis of an ellipse subtends an equilateral triangle with vertex at one end of major axis, then write the eccentricity of the ellipse.

What is the 20th term of the sequence defined by $a_n = (n - 1) (2 - n) (3 + n)?$

Write the component statements of the following compound statements and check whether the compound statement is true or false:
To enter into a public library children need an identity card from the school or a letter from the school authorities.

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow{4}}\frac{\text{x}^2-16}{\sqrt{\text{x}}-2}$

If a coin is tossed two times, describe the sample space associated to this experiment.

Solve: 3x + 8 >2, when x is an integer.

Find the derivative of $\frac { x + \cos x } { \tan x }.$