Question

What is the value of

Answer 1

\[\Huge \sum_{r=1}^{n}a\]
a is any arbirtary constant..just a general question

Answer 2

it is na

Answer 3

how?

Answer 4

Simply it says that you must add up a for n times. a + a + a + a + ...... + a + a = na

Answer 5

\[\Huge \sum_{r=1}^{n}r \neq rn\]
?

Answer 6

the summation from 1 to N of "template"
means template is replicated N times, with a plus sign in between terms

if the template has any "r"s in it, the r's are replace with 1, 2, ... N in each term

Answer 7

This summation is a different thing. Because r isn't constant here.

Answer 8

in your last example, where the template is a single "r"
you get
1+2+3+...+N
because you replace each r with successive values from 1 to N

Answer 9

if the template was A*B^r
you would get A*B^1 + A*B^2 + .... + A*B^N

Answer 10

if the template has no r's such as A
you would get A+A+...+A N times

Answer 11

so mathematically?
\[\Huge \sum_{r=1}^{n}a=\Huge a\sum_{r=1}^{n}1\]
but there is nothing left to sum :/

Answer 12

if the template is 1, you would get 1+1+1+...+1 N times

Answer 13

template is replicated N times, with a plus sign in between terms

Answer 14

okay!thanks..got it :D

Answer 15

Suppose a-r=a is a constant sequence, now summation would be:

\[\sum_{n=1}^{N} a_r = a_1 + a_2 + a_3 + ... + a_N = a + a + a + ... + a = na\]

Answer 16

yup clear