Question

The sum of 1+3+5+7...upto n terms is​

Answer 1

a = 1

d= 2

n = nth term...

therefore,

a+(n-1)d= 1 + (n-1)2

= 1+ 2n-2

2n-1

Answer 2

Answer:

Step-by-step explanation:

1 + (-3 + 5) + (-7 + 9) + (-11 + 13) + (-15 + 17) + (-19 + 21) + …

simplifies to:

1 + (2) + (2) + (2) + (2) + (2) + …

which further simplifies to the number of terms in your expression:

3 = 1 + (-3 + 5)

5 = 1 + (-3 + 5) + (-7 + 9)

7 = 1 + (-3 + 5) + (-7 + 9) + (-11 + 13)

9 = 1 + (-3 + 5) + (-7 + 9) + (-11 + 13) + (-15 + 17)

11 = 1 + (-3 + 5) + (-7 + 9) + (-11 + 13) + (-15 + 17) + (-19 + 21)

etc.

In other words, if there are an infinite number of terms in your expression, this sum would simplify to:

∞

(1 - 3) + (5 - 7) + (9 - 11) + (13 - 15) + (17 - 19) + …

simplifies to

(-2) + (-2) + (-2) + (-2) + (-2) + …

which further simplifies to the negative of the number of terms in your expression:

-2 = (1 - 3)

-4 = (1 - 3) + (5 - 7)

-6 = (1 - 3) + (5 - 7) + (9 - 11)

-8 = (1 - 3) + (5 - 7) + (9 - 11) + (13 - 15)

-10 = (1 - 3) + (5 - 7) + (9 - 11) + (13 - 15) + (17 - 19)

etc.

In other words, if there are an infinite number of terms in your expression, this sum would simplify to:

-∞