Progression

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1.Find the fallacy :-
n+n+n.....(n terms)=n²
differentiating both sides w.t.n
1+1+1....n terms=2n
n=2n
1=2
guess: can we differentiate both sides on an identity.
2.find the sum:-
1+(1+a)r+(1+a+a²)r²+..n terms
3.Find the sum
1.1!+2.2!+3.3!+4.4!+5.5!...n terms

#Mathematics #Algebra

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1 Answers

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Abhishek Ghosh ·2009-08-20 07:06:14

1. Fallacy : You can differentiate wrt to a continuous variable, not a constant.

2. mth term is

r^m-1(a^m-1-1)/(a-1)

take out 1/(a-1) and sum the rest, it is a GP

3. Each term can be written as (m+1)! - m!

The sum is (n+1)! - 1

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