Question

write the series with summation notation.
2+5+8+11+ . . .

Answer 1

so you need to find n'th term first
do u notice any pattern ?

Answer 2

THERE IS A CERTAIN PATTEN..OF 2+(2+3)+(2+3+3)+(2+3+3+3)....
WRITING IN SUMMATION IT WILL BE \[\sum_{1}^{N}2+\sum_{1}^{N-1}3\]

Answer 3

thats not totally correct...first of all, its an infinite series....

Answer 4

DOES THE QUESTION GIVES ANY INTEL ABOUT THAT? WELL THEN I AM CORRECT IF ITS FOR N TH TERMS..

Answer 5

The sum doesn't work
you can test it out yourself

Answer 6

the pattern is +3

Answer 7

correct!
so we can say the common difference between the terms = d = +3

Answer 8

first term = a = 2

now use the formula for n'th term of this arithmetic series as
\(\large a_n = a +(n-1)d\)

Answer 9

then you can put that a_n in sum notation as
\(\Large \sum \limits_1^\infty a_n\)

Answer 10

try it ?

Answer 11

\(a_n = 2+(n-1)\times 3= 3n-1 \\ so, \sum \limits_1^\infty (3n-1)\)
thats it!

Answer 12

that's the answer?

Answer 13

yes

Answer 14

is it correct? I have a picky teacher :( lol