Question

k=1 sigma k tends to infinity ((1/2^k)-(1/2(k+1))) how can calculate the sum of this series..?

Answer 1

is it geometric or telescopic?

Answer 2

first write out a few terms of the series, so term where k=1 + term where k=2 + term where k=3

Answer 3

terms*

Answer 4

looks like it is a geometric telescope

Answer 5

bro this is geometric series na..?

Answer 6

then write out both terms, and find some way to cancel stuff between the two, then the sum should be clear.

Answer 7

if its geometric the term2/term1 will = term3/term2
if this is so, then find that number and do the equation for geometric. I forget it but its something like a/(r-1) or something like that.

Answer 8

where a is the first term , and r is that number we got by devind ratios. I think thats it but your book should define it.

Answer 9

how can calculte tthe sum can u help me.?

Answer 10

did you write out the series?

Answer 11

no..:(

Answer 12

do it then its easy, replace k with 1 1/2 -1/4 then k = 2 1/4 - 1/6 ... and you get
1/2-1/4+1/4 -1/6...this looks telescopic because the 2nd and third term cancel

Answer 13

yup..
then..?

Answer 14

hellow r there

Answer 15

hello any one see my qus