मान लीजिए कि ∑ an एक अनंत श्रेणी है जहाँ an > 0 है। निम्नलिखित में से कौन सा कथन असत्य (FALSE) है?

The value of ∑ k=1∞ (-1)k+1 k(k+1)k! is:

The sum of the infinite series (13 + 47) + (132 + 13 × 47 + 4272) + (133 + 132 × 47 + 13 × 4272 + 4373) + ... up to infinite terms is equal to:

The series 1p + (1/2)p + (1·3 / 2·4)p + ... is ___________.

The alternating series ∑n = 1∞ (-1)n + 1log(n + 1) is:

Which of the following is a convergent series?

Match List-I (Infinite Series) with List-II (Nature of Series) and choose the correct option: List-I: A) 12 - 7 - 3 - 2 + 12 - 7 - 3 - 2 + ... B) 1 - 1/2 + 1/3 - 1/4 + ... C) ∑n=0∞ {(n3+1)1/3 - n} D) ∑n=1∞ 1 / [n(1 + 1/n)] List-II: I) Convergent II) Oscillatory III) Divergent IV) Conditionally convergent

Find the sum of the infinite series: 1 + 415 + 4 × 1015 × 30 + 4 × 10 × 1615 × 30 × 45 + ... ∞

If the infinite series 1 • 2 • 3 ... n4 • 7 ... (3n+1) xn (where x > 0) is convergent, then according to Ratio Test, which of the following intervals or values for x must be true?