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|dw:1440601651278:dw|

you want to solve for \(n\) in :
\[2^n-1 = 63\]

is the answer 6

no wait, they made it tricky

lets do it step by step

forget that link, it would be easy if u try it on ur own

how good are u with pascal triangle ?

i just only know how to form a pascal triangle
1
121
1331...

lets review one important result of pascal triangle quick

see the pattern ?

yes

can you guess the sum of entries in 100000th row ?

\(2^{99999}\) ?

|dw:1440602644567:dw|

i didnt understand , do u mean i need to start couting from second row

now we can say that the sum of entries in \(n\)th row is \(2^n\)

ok if we count from the second row as row 1

Exactly, in other words we're starting our count for rows from 0,1,2,...

instead of 1,2,3,...

ok

so when somebody asks you to look at "3"rd row of pascal triangle, they really mean the 4th row ok

yes i get that.

sum of 6th row =\(2^{6}\)
sum of 7th row =\(2^{7}\)

good, how is pascal triangle related to combinations/counting ?

i don't knw

suppose you have \(6\) objects
how many total ways are there to choose 2 out of them ?

6C2

simplify, what is the number

15

Yes, now look at the 6th row in pascal triangle :
|dw:1440603215894:dw|

suppose you have \(6\) objects
how many total ways are there to choose 3 out of them ?

20

you can guess, it is there in pascal triangle :
|dw:1440603390646:dw|

yes

\(\large \binom{6}{4}\) is the number locatd at 4th position in 6th row
(we count from 0)

using pascal's triangle, can you tell the value of \(\dbinom{7}{5}\) ?

yes it is same as \(\binom{6}{2}=\binom{6}{4}\)

Yes, it has that symmtry
the values in left half are same as the values in right half

7th row 5th number or 2nd number

what is it

can you highlight the number

sry it was sry it was 3ed number 21

\(\dbinom{7}{5}\) is the 5th element in 7th row :
|dw:1440603778591:dw|

so basically you want to solve :
\[\large \dfrac{2^{2n+1}}{2}-1 = 63\]

yea u told that