Question

What is the vaue of 1+2+3+4+5+......+infinity.?

Answer 1

★ THEORY OF NUMBERS ★

Simply if any series is extended to infinity , it may result up in any value if it's in GEOMETRIC PROGRESSION , but we can't say anything about the series if it's executive in ARITHMETIC PROGRESSION as above ...


Let's consider the system :

1 + 2 + 3 + 4 + ...+ n + ... ∞

For the sum upto n

It's defined as , n ( n + 1 ) / 2

For it's INFINITY extension , we can only pre define the behaviour of series end up results as , it'll be the largest number consequently increasing function series , and will result in INFINITY

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Answer 2

this is an example of A.p

taking a as 1 d as 1

we get Sn as (n×[n+1]) ÷ 2