Question

find sum to n terms of the series
1.2+2.2^2+3.2^3+.... to n terms

Answer 1

\[\sum_{i=1}^{n}i \cdot2^i\]

Answer 2

the answer given is 2+ (n-1) 2^(n+1) ... how to get this ??

Answer 3

is it 1.2 2.2^2 3.2^3
or 1, 2^2, 3^3 ???

Answer 4

it is 1.2 2.2^2 3.2^3

Answer 5

\[\sum_{i=1}^{n}i \cdot 2^i=2^n \sum_{i=1}^{n}\frac{i}{2^{n-i}}\]

and ehuman, it's not an arithmetic series

Answer 6

geometric my bad

Answer 7

not quite geometric either

Answer 8

Sum of series is
\[Sn=n/2*(2a(n-1)d)\]

Answer 9

it is a arithmetico - geometric series .... yes i know the rules, somehow not getting the answer.. the answer given is 2+ (n-1) 2^(n+1) ...so if you post the solution completely i will understand how you did it

Answer 10

close though

Answer 11

Let
\(\large S_n = 1\cdot 2 + 2\cdot 2^2 + 3\cdot 2^3 +\ldots +n\cdot 2^n\).
Then it follows that
\(\large 2S_n = 1\cdot 2^2+2\cdot 2^3+3\cdot 2^4+\ldots +n\cdot 2^{n+1}\)
Now consider \(\large 2S_n - S_n\) and simplify that difference. You should get the formula you're looking for.

Can you take things from here? :-)

Answer 12

@ChristopherToni : thanks a lot .. i got the answer :)