# Trying to prove this equality involving a summation of a binomial coefficient.

#### jdinatale

I immediately thought of induction, so that is what I used, but I can't seem to make any progress past a certain point.

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#### tiny-tim

Homework Helper
hi jdinatale!

(i haven't looked at your induction proof , but …)

why not just multiply the LHS by n+1 ?

#### jdinatale

hi jdinatale!

(i haven't looked at your induction proof , but …)

why not just multiply the LHS by n+1 ?
Ok, I tried that and I eventually could not go any further. Any ideas on what's going wrong?

#### tiny-tim

Homework Helper
hi jdinatale!

in the third line you have ∑k=0…j j+1Ck+1

put m = k+1, that's ∑m=1…j+1 j+1Cm

what is that?

#### jdinatale

hi jdinatale!

in the third line you have ∑k=0…j j+1Ck+1

put m = k+1, that's ∑m=1…j+1 j+1Cm

what is that?
Brilliant! I've solved the problem now, thank you so much. But please tell me, how did you possibly know to do that? That was not obvious to me at all, and I'm not sure how you would just know to do that.

#### tiny-tim

Homework Helper
easy!

the clue was in the question …

the RHS said 2n+1,

which i know is ∑ n+1Cr

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