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10. Prove that if (un) is a sequence for which lim(un – Un-1) Un :l, then lim = l. 1 11. Let (um) be a sequence of strictly positive numbers. Show that Un+1 (a) lim = l lim Vun = l. Un (b) lim un — е lim Vuju2... Un = l. 12. Show that n 1 27 1 (b) lim - T[(2+ k)*/m . 1 (a) lim -I[(2n + k)!/n 4e n k=1 n k=1 e 13. Calculus limit of the following sequences. 1 (а) ап — 1 (b) fn PE N. p+1' k=1 k=1 14. Prove that n 1 na+1 (a) (a < -1), ~ In n, k k=1 a +1 k=n n n In n ni-a, na+1 In k (b) > ka ~ (a > -1), (d) > (a < 1), a +1' ka k=1 1 - a k=1 =WI WI

10. Prove that if (un) is a sequence for which lim(un – Un-1) Un :l, then lim = l. 1 11. Let (um) be a sequence of strictly positive numbers. Show that Un+1 (a) lim = l lim Vun = l. Un (b) lim un — е lim Vuju2... Un = l. 12. Show that n 1 27 1 (b) lim - T[(2+ k)*/m . 1 (a) lim -I[(2n + k)!/n 4e n k=1 n k=1 e 13. Calculus limit of the following sequences. 1 (а) ап — 1 (b) fn PE N. p+1' k=1 k=1 14. Prove that n 1 na+1 (a) (a < -1), ~ In n, k k=1 a +1 k=n n n In n ni-a, na+1 In k (b) > ka ~ (a > -1), (d) > (a < 1), a +1' ka k=1 1 - a k=1 =WI WI

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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10. Prove that if (un) is a sequence for which lim(un – Un-1) Un :l, then lim = l. 1 11. Let (um) be a sequence of strictly positive numbers. Show that Un+1 (a) lim = l lim Vun = l. Un (b) lim un — е lim Vuju2... Un = l. 12. Show that n 1 27 1 (b) lim - T[(2+ k)*/m . 1 (a) lim -I[(2n + k)!/n 4e n k=1 n k=1 e 13. Calculus limit of the following sequences. 1 (а) ап — 1 (b) fn PE N. p+1' k=1 k=1 14. Prove that n 1 na+1 (a) (a < -1), ~ In n, k k=1 a +1 k=n n n In n ni-a, na+1 In k (b) > ka ~ (a > -1), (d) > (a < 1), a +1' ka k=1 1 - a k=1 =WI WI
Transcribed Image Text:10. Prove that if (un) is a sequence for which lim(un – Un-1) Un :l, then lim = l. 1 11. Let (um) be a sequence of strictly positive numbers. Show that Un+1 (a) lim = l lim Vun = l. Un (b) lim un — е lim Vuju2... Un = l. 12. Show that n 1 27 1 (b) lim - T[(2+ k)*/m . 1 (a) lim -I[(2n + k)!/n 4e n k=1 n k=1 e 13. Calculus limit of the following sequences. 1 (а) ап — 1 (b) fn PE N. p+1' k=1 k=1 14. Prove that n 1 na+1 (a) (a < -1), ~ In n, k k=1 a +1 k=n n n In n ni-a, na+1 In k (b) > ka ~ (a > -1), (d) > (a < 1), a +1' ka k=1 1 - a k=1 =WI WI
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