Find the sum of the digits of the number 6+66+666+6666 + ... +666...66, where the last number contains 100 digits.

Sum of the digits of the number

Step-by-step explanation:

Step(i):-

Given series

6+66+666+6666 + ... +666...66 up to 100 digits

Taking common '6'

6 ( 1 + 11 +111+ 1111+1111+.................11111....11 100 digits)

Multiply '9' and divisible by'9'

Multiply inside '9'

Step(ii):-

we know that sum of geometric series

we know that

a + a + a+........n terms = n a

 ....(i)

The sum of the 100 digits in geometric series

Now the equation (i)

The sum of the digits of the number  

Final answer :-

Sum of the digits of the number

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2