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श्रृंखला के n पदों का योग 1 + (1+ 2) + (...

श्रृंखला के n पदों का योग 1 + (1+ 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4)....... | 12 | अनुक्रम और amp; एस...

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(1) / (1.2) + (1.3) / (1.2.3.4) + (1.3.5) / (1.2.3.4.5.6) + .... oo

lim_ (n rarr oo) [(1) / (1.2) + (1) / (2.3) + (1) / (3.4) + ... + (1) / (n (n + 1))] =

lim_ (n rarr oo) (1+ (1) / (2) + (1) / (2 ^ (2)) + (1) / (2 ^ (3)) + ...... (1) / (2 ^ (n))) / (1+ (1) / (3) + (1) / (3 ^ (2)) + (1) / (3 ^ (3)) ...... (1) / (3 ^ (n)))

I fcos ^ (- 1) x / a + cos ^ (- 1) y / b = (5pi) / 12andsin ^ (- 1) x / a-sin ^ (- 1) y / b = pi / 12t hen ( x ^ 2) / (a ^ 2) + (y ^ 2) / (b ^ 2) = 1) 12) 1 & sol43) 3 & sol4

Let P_ (n) = (2 ^ (3) -1) / (2 ^ (3) +1) * (3 ^ (3) -1) / (3 ^ (3) +1) * (4 ^ ( 3) -1) / (4 ^ (3) +1) ...... (n ^ (3) -1) / (n ^ (3) +1) Prove that lim_ (n rarr oo) P_ ( n) = (2) / (3)

lim_ (n rarr oo) (1.2 + 2.3 + 3.4 + .... + n (n + 1)) / (n ^ (3))

If A = [(1,2),(3,4)] , then 2A^(-1)=

Sum the series : (1*2)+(1*2+2*3)+(1*2+2*3+3*4)+... to 12 brackets.