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Find the sum 1/(k^2+1) from k = 1 to infinity

Give sum 1/k^2 = pi^2/6, sum 1/k^4 = pi^4/90, sum 1/k^6 = pi^6/945 all from k = 1 to infinity

i know sum 1/(k^2+1) = sum (1/k^2 - 1/(k^2*(k^2+1))) = sum 1/k^2 - sum 1/(k^2(k^2+1))

= pi^2/6 -sum (1/(k^4+k^2))

i dont know what to do from here,

can anybody help me on this, Thanks

A nozzle on a hose accelerates water from 4 cm diameter to 1 cm diameter. The

pressure upstream from the nozzle is 400 kPa, what is the maximum velocity exiting

the nozzle?

Just give the direction how to do the problem , I was so busy at work for summer and totally forgot what i had been studied.

Thanks

A bent coin turns up heads with probability .62 . the coin is tossed 12 times

a) number of ways that ne may arrange 4 letters H and 3 letters T into a line ?

is it C(12,4)+C(12,3)?

b) what is the probability of sequence HHHH TTT

is it C(12,4)* (.62)^4*(1-.64)^8 + C(12,3)*(1-.62)^3*(.62)^9?

c) what is probability of sequence HHHTHTT

d) The aggregate probability of all sequences that have four H and three T

Thank you . I m so bad at probability i need your help

i built the website for my class, i already did all the part , but i didnt have any ideas on my background. i want it to have something about school such as picture of school, etc..........., i didnt have any picture ,so i hope you guys can help me on it,

plz give me a website to hav some kinds of picture i can build the website

what do you do afther you graduate for nuclear engineering?

how many kinda jobs will be working with nuclear

can you have a jobs when you done with school?

i have a laptop sony vaio, i upgraded the window vista about 3 months ago,everything was ok so far. the problem i had on window media player(11), sometimes it worked and sometimes it didnt work i dont really know what was wrong , i got help from sony support but they gave me some shits which didnt do anything.

when i clicked on window media player i dont see any screen coming out, so i cant even play any music on window media. one thing is so weird when i opened the control panel to look for window media i want to uninstall that and reinstall but they didnt let me to uninstall . i dont know how to fix it, i hope you guys can help me out, i appreciate that

once again thanks for any participates