This is a geometric progression with a=13 to the power of 5, r=1/13 and n=6. Sum of geometric progression is a(1-r to the power of n), divided by 1-r. Or, writing the terms in the opposite order, a=1, r=13, n=6. Sum is a(r to the power of n, minus 1) divided by r-1. The answer will be the same and using this formula is quicker.
If one has to crank through r to the power of n here, why not just do repeated long multiplication to get the powers of 13 from 13^0 through 13^5 and then add those six numbers. That'll beat having to do a long division, if this is on paper.
This can be done faster using long multiplication by 13, in my case in just over 2 minutes. Would be interesting to know what the Harvard interviewers were looking for.
This is a geometric progression with a=13 to the power of 5, r=1/13 and n=6. Sum of geometric progression is a(1-r to the power of n), divided by 1-r. Or, writing the terms in the opposite order, a=1, r=13, n=6. Sum is a(r to the power of n, minus 1) divided by r-1. The answer will be the same and using this formula is quicker.
If one has to crank through r to the power of n here, why not just do repeated long multiplication to get the powers of 13 from 13^0 through 13^5 and then add those six numbers. That'll beat having to do a long division, if this is on paper.
@@SeekingTheLoveThatGodMeans7648 true, this could be done too as there are only 6 terms
Perfect teaching method
Well done Maam
Very well explained
Nice trick and solution
Much needed this type of olympiad problems
13⁵ + 13⁴ + 13³ + 13² + 13¹ + 13⁰ = (13⁶ − 1) / (13 − 1)
13 * 13 = 169
169 * 13 = 2197
2197 * 2197 = 4826809
4826808 / 12 = 402234
Alternatively you can use the Horner scheme:
1 + 13 = 14
1 + 13 * 14 = 183
1 + 13 * 183 = 2380
1 + 13 * 2380 = 30941
1 + 13 * 30941 = 102234
good 👍
Short and sweet explanation
This can be done faster using long multiplication by 13, in my case in just over 2 minutes. Would be interesting to know what the Harvard interviewers were looking for.
Very much effective teaching
Nice explanation
Correct answer
Very effective teaching