Quick question: -tsudzukeru and -miyou endings?
I've seen these endings used in some places, the first one as in

a) sumitsuzukeru (what's the verb here?)
b) sagashitsuzukeru (from 'sagasu', right?)

according to dictionary:
続ける【つづける】 (v1,vt) to continue; to keep up; to keep on; (P)

what would these both examples translate to, then? (as an added note, i had a lot of problems searching for that word... i kept searching for 'tsuzukeru' without any avail... now that i think of it, i had RARELY ever seen 'du' and 'di' used in hiragana... i was kinda confused when i saw it.)

and the second one as in

c) mitemiyou

i had translated it as 'let's give it a try', but what's the real meaning? can it be replaced by '-mashou'?

thanks :)

Question

Quick question: -tsudzukeru and -miyou endings?
I've seen these endings used in some places, the first one as in

a) sumitsuzukeru  (what's the verb here?)
b) sagashitsuzukeru  (from 'sagasu', right?)

according to dictionary:
続ける 【つづける】 (v1,vt) to continue; to keep up; to keep on; (P)

what would these both examples translate to, then? (as an added note, i had a lot of problems searching for that word... i kept searching for 'tsuzukeru' without any avail... now that i think of it, i had RARELY ever seen 'du' and 'di' used in hiragana... i was kinda confused when i saw it.)

and the second one as in

c) mitemiyou

i had translated it as 'let's give it a try', but what's the real meaning? can it be replaced by '-mashou'?

thanks :)

Answer

a)
sumitsuzukeru (sumitsudukeru is a right spell of hiragana, you know.)
sumi tsudukeru. 住み続ける, verb is 住む, sumu, live.

彼は10年間そこに住み続けた
kare ha 10nenkan soko ni sumi tsuduketa.
He had continued to live there for 10 years.

b)
sagashitsuzukeru
sagashi tsudukeru. 探し続ける, verb is 探す, sagasu(you correct), search.

あなたは長い時間その言葉を辞書で捜し続けた.
anata ha nagai jikan sono kotoba wo jisho de sagasitsuduketa.
you had continued to search the word using dictionary for long time.

～続ける emphasis a state or an action is continue.
naki tsudukeru, 泣き続ける, verb naku, cry.
hartaraki tsudukeru, 働き続ける, verb hataraku, work
aruki tsudukeru, 歩き続ける, verb aruku, walk

c)
mitemiyou
mite miyou, 見てみよう
let's try to see.

you can replace "miyou" to "mimashou".
"mite mimashou". its polite expression than "mite miyou".